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# Structural Vibration - Science topic

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Questions related to Structural Vibration
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How can I get the second and third natural frequency of a cantilever beam experimentally??
The problem that I am facing is that I got only the first natural frequency.. I can't get other frequencies..
To expand on the answer provided by Vyacheslav Ryaboy, when performing the increasing-frequency sine sweep test, you would pass through the first resonance frequency of the cantilever beam. This is what is referred to as "hitting" the first resonance frequency. If you continue to increase the frequency, you will eventually reach and pass through the second resonance frequency. If you continue to increase the frequency further, you will eventually reach and pass through the third resonance frequency.
Depending on the equipment at your disposal, you may wish to use an impact hammer to simultaneously excite a number of modes of vibration. The measurement system would likely have the ability to compute the transfer function between the response and the excitation force. The frequency response curve would generally show the first few natural frequencies of vibration of the cantilever beam, dependent somewhat on the bandwidth of the force impulse and also the point of application of the transient excitation force.
The links provided by Om Prakash Chhangani and Mohamed-Mourad Lafifi give the formulas for the first three natural frequencies of a cantilever beam, as well as a graphical representation of the associated mode shapes. There are some suggestions for how to go about experimental testing there too.
What test equipment do you have available to conduct the experiments with?
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How to represent natural frequencies and mode shapes in same matrix for many cases for damage detection purposes?
As Christian Willberg already pointed out, a 2 DOF system can only have 2 eigenvalues and consequently 2 mode shapes. These mode shapes describe all possible movement/displacement fields of the system. That is to say, each system response is a linear combination of those 2 modes. Everything else is not possible. Thus, if you have 3 modes shapes you must have a 3 DOF system.
In the modal decomposition method, the modes can be used to decouple the equations of motion (provided that we fulfill certain assumptions with respect to the material damping).
Therefore, you must restate your question and provide more details on your system, if you expect a meaningful answer. At this point, the question you would like to be clarified is not physical. Please go back to your problem and think a bit about what you actually want/need to know.
Kind regards,
Sascha
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I have the following questions regarding vibration-based damage detection of a cantilever beam:
1-What is the purpose of discretizing the cantilever beam by finite element technique?
2-Do the number of discretized elements and their length affect the modal analysis( healthy and damaged natural frequency, mode shapes)?
3- Why do the biggest changes in natural frequency happened when the damage occurred near the fixed end and became smaller if the damage occurred far away from its fixed end?
The reduction in stiffness will be high if the defect/crack is present in regions of high stress. In a cantilever beam, the maximum stress occurs at the fixed end. Therefore, if the defect/crack is near the free end you can expect a greater reduction in the natural frequency from that of an undamaged beam as compared to when the defect/crack is present elsewhere. You can find a discussion on the same in my research article. I have attached it below for your perusal.
Hope it helps.
Regards,
Jatin
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What is lattice mode in RAMAN vibration mode? In general, can you help me about what the lattice mode is in the RAMAN analysis?
I'm working on Sb2S3 thin films. During the Raman analysis, I saw that there are lattice mode vibrational modes. How is it different from symmetric S–Sb–S stretching or symmetric S–Sb–S bending? In General, can you help me about what the lattice mode is in the RAMAN analysis?
Thank you so much for your reply, and have a nice day. Best regard.
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It is recommended to calibrate the measuring instruments before performing any experiment. Ideally, how often do we need to calibrate an accelerometer? Are there any simple and effective methods for calibrating accelerometers in the laboratory without seeking professional assistance?
Stick the accelerometer to a weight of known mass. Excite the weight with a known force using instrumented hammer or shaker. The acceleration and force will be related by F=ma. If you know the mass m, you can work out an appropriate calibration factor quite easily.
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Hello Researchers,
The FEM discretized (meshed) geometry/domain is considered stiffer than the actual geometry/domain due to the assumption of variation of the displacement within each element. This is analogous to the displacement being constrained to vary in a particular fashion within each of the elements. This results in the stiffness of the discretized domain being greater than the actual domain. As the element size decreases (or the number of elements increases), the constraint on the displacement loosens due to the smaller size of the element and hence, the smaller constraint zone. Thus, the stiffness of the meshed domain decreases and approaches that of the actual domain as the number of elements is increased.
Based on the above reasoning, the natural frequencies (on increasing the number of elements) must converge from above to the actual value (i.e. converge from higher values to the actual value).
1. Can this be considered to be strictly true?
2. Has any deviation from it been observed (i.e. convergence from below or lower values to the actual value) and if so how can that trend be physically explained/interpreted?
Dear Jatin,
Not always does a finer mesh result in a more exact solution. A mesh convergence study should always be performed to guarantee the descending trend of the error as the mesh size gets smaller.
Having this verified, yes, a finer mesh reduces the stiffness of the model. Because FE approximates the the PDE solution by forcing the element into specific modes of displacement which yields a stiffer element. But as the element size decreases, the FE solution converges to the analytical solution of PDE.
Eigenvalue can be physically interpreted as how stiff the structure is in the eigenvector direction. So it follows the same pattern as stiffness.
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I'm looking for some guidance and advise in the subject of "Machine Learning," which I'll utilize for my research interests in computational mechanics and structural vibration control.
@ Rachid Ait Maalem Lahcen,
Thanks for your valuable suggestion. Are there any literature available for machine learning which is used in computational mechanics or structural vibration control?
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In the article by Yang et al. (2004) [1], they said the total mass of the structure is 153000 t. However, in another article by Patil and Jangid [2], they consider the mass of the building to be 150000 t. Moreover, using the matlab files [3] and calculating the sum of effective modal masses, I found 210862.7 t.
[1] Benchmark Problem for Response Control of Wind-Excited Tall Buildings. Jann N. Yang; Anil K. Agrawal; Bijan Samali; and Jong-Cheng Wu
[2] Optimum Multiple Tuned Mass Dampers for the Wind Excited Benchmark Building. Veeranagouda B. Patil a & Radhey Shyam Jangid
The masses are given as none diagonal form therefore you can not sum up them. 153000 t is accurate.
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Dear Research scholars,
I was doing my MTech thesis on pendulum based TMD and I was having trouble defining the link properties. I even followed the tutorials put on CSI website. still, I wasn't able to properly do that.I would be very grateful if anyone helped me with this.
Thank you
Dear Yathish
Within SAP2000 or ETABS, a TMD may be modeled using a spring-mass system with damping. Guidelines for this subsystem are described in the following link:
Regards,
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Hello everybody
Despite a few TMD cost models available in the literature, I am searching for more accurate initial and lifetime cost models of translational TMDs for Life Cycle Cost Analysis (LCCA) of TMD-equipped structures.
In fact, the provided cost model affiliated with one of the companies designs and manufactures transitional TMD (such as LeMessurier CO.), which this model consists TMD initial cost (construction and installation of the TMD) and TMD damage cost (maintenance and repair losses of TMD before structural collapse)
The effectiveness of tuned mass dampers (TMDs) in reducing the seismic response of civil structures is still a debated issue. The few studies regarding TMDs on inelastic structures indicate that they would perform well under moderate earthquake loading, when the structure remains linear or weakly nonlinear, while tending to fail under severe ground shaking, when the structure experiences strong nonlinearities. TMD seismic efficiency should be therefore rationally assessed by considering to which extent moderate and severe earthquakes respectively contribute to the expected cost of damages and losses over the lifespan of the structure.
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In ultrasonic assisted machining, ultrasonic welding etc. systems, transducers are required to vibrate in eigenfrequency . If we vibrate a system at its natural frequency ( eigenfrequency ), won't there be resonance? Why do we want to vibrate in mode shapes ( eigenfrequency )?
Likely to be desired to use the tranducers at resonance to emit maximal amounts of energy.
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Dear researches
In general, the value of modal participating mass ratio (MPMR) for each vibration mode represents the participation of each mode in the structural responses.
when a structure equipped with TMD, a vibration mode is added to the others. MPMR value of the added vibration mode can be significant even when TMD mass is very small and as a result, TMD has no effect on the structural responses.
How can this contradiction be justified?
I second Einar Strømmen & Pranoy Nair responses, also I would like to add a point that when we add a TMD we are introducing damping into the system. I am not really sure how you would define MPMR in such a system as modal analysis works only for undamped systems.
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Can anyone suggest a data compression algorithm to compress and regenerate data from sensors(eg. accelerometer-it consists of time & acceleration) that are used to obtain structural vibration response?I have tried using PCA but i am unable to regenerate my data.Kindly suggest a suitable method or some other algorithm to go with PCA?
Saranya Bharathi I am wandering , which algorithm did you use ?
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Weight drops generates vibrations in the floor they hit. Impulse mdv must be conserved, even if the floor or mass is cushioned with mats. Cushioning leads to less high frequency content in the resulting impulse noise and impact. Does that also lead to a higher content of lower frequency energy in the resulting floor noise and vibrations?
Hi Anders
Contact time, as indicated in your title, matters. That said, I tend to balance energy rather than impulse. See below for some ramblings.
As a rule of thumb, for an effective contact time, dt, the force spectrum is flat up to the frequency 1/dt and contains 90% of its signal energy below 2/dt.
So, yes, you do concentrate energy into a lower frequency range.
At the same time, bag mass, M, has the velocity, V, and the kinetic energy, M*V2/2, directly before impact. The kinetic energy is handled by the flexible buffer with stiffness K and the potential energy KX2/2. This yields, X = sqrt(M/K)*V.
We see that for a given impulse velocity, V, the higher the mass and the softer the spring, the larger the buffer compression stroke, X. As force is F = K*X, we find also that F = sqrt(K*M)*V and hence, the stiffer the spring and the higher the mass & velocity, the higher the maximum impulse force.
The stroke, velocity and contact time (simplistically) relate as X = V*dt/2 as dt is the time require to reach the stroke X and as 2/dt describes 90% of the total force.
We tend to find that the larger the stroke and the longer the contact time, the lower the contact force and the lower the frequency range that is excited.
The above assumes a perfectly linear spring. Buffer stops tend to be nonlinear which is why Force-Displacement curves tend to be provided for such components.
Now, to further compound matters - we need to take a look at shock response. Long story short, shock theory tells us that we get the highest dynamic response when the contact time, dt = Tj/2, where Tj is the mode j period time.
A soft mat tends to help, though you may be unfortunate and end up shaping the pulse for maximum dynamic response.
So, as per usual - it depends.... ;)
Hope this helps
Claes
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I am studying the solid-liquid interfaces. I created the solid-liquid coexistence system by combing solid part and liquid part with the same sectional areas together. Then the atoms in the solid were fixed, while the atoms in the liquid were allowed to move freely. The whole system reached equilibrium at a temperature above the melting point of the liquid. Then the system was slowly cooled down to a temperature below the melting point, which caused the liquid solidify. The problem was that the layers in the solidified structure as a whole move forward and backward in a plane parallel to the original solid-liquid interface. Why don't atoms in the solidified structure vibrate around their equilibrium sites? Why do they mainly move forward and backward along a particular direction?
Rui Yan, were you able to resolve this behaviour? I'm encountering a really similar problem!
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I am currently working on a project which ask me to look for the natural frequency of engine girder structure. This is to ensure that the excited frequency from the engine does not coincide with the natural frequency of the structure. The engine is running at 1900RPM.
However, i am kinda lost because when i run the model using Modal analysis, The range of frequencies for 5 modes are only 1-5Hz, i would have to run around 1000 modes in order to reach 1900 RPM. Am i doing something wrong or is this the case? The structure is made up of around 20 shells.
I appreciate any help. Thanks.
Hello Daniel, FEM is fine to characterize isolated components, but your challenge relate to the boundary conditions ! Your very low frequency modes relate to bending + torsional motions of your girder flying in the air, while they will be constrained by the coupling with the ship hull which ultimately sits on water. The uncertainty on all these boundaries makes IMPOSSIBLE to trust a FEM model at >30Hz (= >1800rpm). In addition, assuming your engine is a Diesel, the most problematic frequency is not the RPM but the firing frequency (6 times higher if you have a 12cylinders engine) ! And if it is a propulsion engine, you have also the gearbox tones... You don't say either if your design uses rubber isolators. It is not impossible to use FEM but it takes years of learning, trials and errors to get the right way to model by FEM such complex structures. FYI a ship as a whole presents several "families" of natural frequencies: "beam modes" of the whole ship (flexure and torsion) at few Hz, local resonances (bulkheads and decks) at some 10 Hz and local resonances (machinery rafts and seatings) up to 100Hz - so there are always possible resonances and this is why silent ship design requires using rubber decoupling and structural damping devices to isolate the sources of vibration. Few shipyards master the whole predictive chain - just remember the Collins Class difficult infancy on this matter !
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I am looking to start working with the isogeometric method to analyze mechanical behavior such as beam, plate, shell and other structures of complex shapes.
can you help me by giving me simple examples in this method and with articles and books that have explanations and applications?
what do you suggest to me and thank you in advance?
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Hi All
How can I define frequency dependent damping in Ansys ?
it seems to be Damping frequency, but I am told that the value I input here, is used only to calculate the stiffness matrix coefficient, so If I input multiple values for damping , they will get overwritten
Number you change according t o your requirement
sample
TB,SDAMP,1,,1 TBFIELD,FREQ,30 TBDATA,1,0.02 TBFIELD,FREQ,70 TBDATA,1,0.018 TBFIELD,FREQ,120 TBDATA,1,0.016 TBFIELD,FREQ,200 TBDATA,1,0.014 TBFIELD,FREQ,240 TBDATA,1,0.012 TBFIELD,FREQ,308 TBDATA,1,0.01
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Good morning
I would like to perform a ground vibration test (GVT) on a wing model. Can a someone suggest a good material on that (including how to perform it)?
The followings are good sources for ground vibration test (GVT):
I hope it is helpful for you.
All the best.
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I am trying to find the resonant modes of a membrane or plate-like membrane, however, this requires a knowledge of the amount of tension on said membrane, specifically in a 2-d sinusoidal distribution of pressure. The only thing I am finding online is the calculation of surface tension of a fluid, or at least something which has a spherical shape, however, I need it for an initially flat solid.
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I have frequency iterations and acoustic amplitude curve. I want to convert it into time vs acoustic amplitude curve. How can I do it using MATLB? Which transfrom required to apply?
You can use Inverse FFT to transform from freq. Domain to time domain as it is your case ..see the attachment
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Dear all,
I am interested in the idea of using AI algorithms in analysing civil structures. Could I connect to any researchers with the same interest? I appreciate all the advice!
Regards,
Hoan Nguyen
Artificial intelligence, Genetic Algorithms (and its variants like Genetic Programming and Gene Expression Programming) are very good tools to use in your research for optimization purpose. I would suggest you to understand the basic concepts first (you can find alot of material regarding this on internet). Also you must have some data in hand before taking a start (data can be yours or secondary data from already published literature). ANN and GEP are the most common techniques used in Civil Engineering and you can goto www.sciencedirect.com and give these keywords.
I have also attached some articles on GEP and ANN which are mostly related to structures.
Hope it helps.
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Is there a way to find the Eigenvectors and Eigenvalues when there is unknown values in a complex damping matrix , using theoretical methods ?
Is it also possible to be done in MATLAB ?
I assume you are referring to FE of a bounded region?
There are two kinds of modes that can be computed, Real modes and Complex modes. The former is standing waves that conserve energy, i.e. with node position (=minimum response) that stand still. The latter uses damping information and describes energy transport across the system and, hence, has node positions that move.
As indicated by their names, real modes have real valued response while complex modes have complex values response.
Real modes can be computed without any damping information.
As indicated by Giuseppe Pennisi damping can be added afterwards with the tacit assumption that it is evenly distributed and light. Other common damping models are viscous modal damping and hysteretic material damping.
The former (viscous) is a weak approximation of sound radiation, the latter (hysteretic) a weak appoximation of internal material friction. The Raleigh damping model mentioned above is used for mathematical convenience and does not originate from any physical damping mechanism.
In real life, damping can be many things. Some ramblings of mine on this topic can be found here https://qringtech.com/2014/06/22/designed-damping-types-mechanisms-application-limitation/
Sincerely
Claes
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There are shell theories like Love's, Donnell-Vlasov, Sander's,etc genrally used. Which theory is applicable here based on the limiting ratio mentioned above ?
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How can I co-relate the response due to the rectangular rod sliding on plate (movement is made by hand) experiment with the mathematical model. The plate is simply supported. The force of excitation is also moving.
Exponential definition of friction coefficient is the most convenient one.
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Ideally using both LaGrangian and Newtonian mechanics I need to conduct vibrational analysis on this system.
The system is structured as such:
Wall - SpringDamper - Rotating component 1 - SpringDamper - Rotating component 2 - SpringDamper - Rotating component 3 - SpringDamper - Wall
I have the equivalent mass moment of inertia for all 3 components and the effective spring stiffnesses of each connecting piece. I also have the To value for the system. These are as follows:
Jd1 = 25.5 kg.m2
Jd2 = 12kg.m2
Jd3 = 9kg.m2
To = 37.5Nm
Anybody have any expertise in this field? Vibrational analysis is something I struggle with and I've never carried it out on a torsional system before.
... attached file.
Best regards
Ch. Oertel
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hello,
In which case and conditions could we consider a 2 DOF system (2 mass 2 springs) like a single DOF system.
thanks
dear. Fikrat Almahdi.
Do you have a PDF file of book: Modal analysis theory and testing ?
could you share to me ?
thank you so much
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I am studying the supersonic flutter characterisitcs of rectangular panels. I am new to this domain and have certain fundamental questions that I am unable to answer. I am employing the Piston theory for determining the flutter boundary, i.e. the flutter speed and the corresponding frequency. I have seen several works in which the v-g (velocity-damping) and v-f (velocity-frequency) graphs are plotted and the critical velocity is determined from the v-g curve corresponding to the point where the damping corresponding to a particular mode crosses from negative to positive region. The velocity (is it correct to say free-stream velocity?) is varied from 0 to a particular velocity of interest.
If I am correct, these v-g and v-f curves are plotted for a particular Mach number (M>1 for supersonic) . If this is the case, I am unable to comprehend why the velocity is varied from zero to a higher value? In most of the papers that I have read, M is defined as the free stream Mach number, M=(free-stream velocity/sonic speed). Is the velocity being varied (from vmin=0 to v) while keeping M (>1) constant?
Any help in clearing these misconceptions would be greatly appericiated.
Thanks
Thank you very much for this resource, Dr. Pany!
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I need to verify my models in ABAQUS, so I need a paper as a reference, what I need is properties of the beam's material, clear thermal loads, and the frequency changes.
here is a link to a review paper that discusses temperature effects on vibration properties of civil structures:
this paper reviews existing literature on the variation of vibration properties of civil structures under changing temperature conditions, mostly bridges though.
As far as I know, depending on the intensity of temperature variation, little frequency changes are observed when the temperature varies in a normal manner. having this in mind, among ambient conditions, temperature holds a high hand, and it's influence on vibration properties is more than others.
you can check the references of the suggested article, or the papers that have cited this article to find more.
Wish you success in finding what you are looking for.
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I need to calculate the analytical relation for frequency of a cantilever composite beam, where one beam is prestressed on which an another non-prestressed beam is placed in a way to form the composite system. Can anyone tell if there is any such analtical expression or hint at possible way of derivation of it.
Thank you. I am trying to model the phenomena of forming a composites using a beam which is already prestressed and having an another beam bonded to it which is non prestressed. And then we perform the modal analysis. Is this problem setup feasible.
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The Elastomeric pads can be used as vibration isolators. I want to know whether there is significant effect of initial compression (pre-loading) of this pads on increasing the dynamic stiffness or it does not worth.
Preload has a huge effect on elastomeric materials. Both tangent and secant stifness change with static preload. Some materials soften, but most of the elastomers generally harden.
When using elastomer pads, usually, the pad producer provides a chart giving the dynamic stifness as a function of force applied (which is generally provided by the weight of the machinery).
Does it worth? Well it depends on what you need to do. Generally, preload on pads can be increased by adding mass between the machin pedestal and the pad itself using blocks of steel or iron. Sometimes it's useful, but you increase stifness together with mass.. hence the system gets tuned nearby the original frequency. In fact, this is usually done to limit the static deflection when loading the machine itself with process material, or to compensate for static misalignment.
To conclude, I wouldn't reccomend to preload mechanically (let's say, with a clamp) the elastomer pad, since creep is relevant for this material. So if you apply preload by imposing a certain displacement, after a while (it can be weeks) your preload force disappear. So with elastomer pads it is important to apply preload by means of constant forces.
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I use Abaqus to model a slender composite structure subjected to dynamic wind actions.
I read in many parts of the literature that Aerodynamic damping exist and could be important for structure which are slender and interact with wind. I am not going into wind-structure interaction at all.
All I need is a convenient and acceptable way of accounting for Aerodynamic damping. From my knowledge on this aspect that the aerodynamic damping coefficient is different from the material/structural damping where a damping ratio is assumed. Instead, it relies on the velocity of the structure and changes with it which is very tedious to incorporate in a Structural Finite Element Analysis procedure.
Please suggest to me from your own experience on how to deal with this issue.
Best Regards,
Mahmoud Alhalaby
Hi Claes,
I almost lost hope that somebody will reply to this question. I am surprised that none of the Aerodynamics researchers on RG commented on this topic which should be quite straightforward for them.
Nevertheless, thank you for the information. Helpful as always!
Regards,
Mahmoud
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I have been working on the PPF controller for a couple of years, and now I want to start some research on the Saturation Controller. I know that both of them are resonant controllers for active vibration control and they have similarities, but what exactly makes them different from each other?
What special characteristics does the SC have which makes it more or less applicable?
Can you introduce some references that have performed a comparison work between these two methods?
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Every time I try, it gives me this error "2 eigenvalues below the shift, Ritz analysis requires all eigenvalues to be above the shift". What can be the problem that makes this error exist?
Dear Abdelrahman Abdelaleem, that warning may be indicative of any modeling error. By default, shift is a very low value. If there are modes below this value, it means there are mode shapes with very low stiffness and, likely, some connectivity problem.
There is a discuss forum on this topic here: http://www.sepakistan.com/topic/1748-ritz-analysis-problem/
I would suggest running some easy tests to check the connectivity. You can also try to use merging
options of nodes. There can be nodes that apparently are connected but they are only close in space and no truly connected.
Hope it may be of any help. Best.
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If a molecule structure is downloaded from chemspider or pubchem, then how to identify point group to do DFT calculations?
Since the identification of point group is very important during the optimization of structure or for vibrational analysis.
Also identification of point group is difficult for long chain molecules.
thank you
regards
M Chaitanya Varma
Hi,
Visualizing software frequently has an option to automatically determine point group (for example I use Chemcraft). On the other hand results of the calculation assuming C1 symmetry should more or less match results of calculation assuming real symmetry of your molecule (but maybe on the larger calculation time).
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When the continuous systems such as string/beam vibrate in an viscous environment, we know that the natural frequencies of the system become damped natural frequencies and there exists a decay constant associated with each of the mode.
Are these decay constants (or damping factors) different for every mode or same? i.e. given an initial condition corresponding to specific modes, will the system decay down in same amount of period?
The question is raised due to this:
When string vibrates in viscous environment, the equation can be written as,
rho*w,tt+c*w,t-Tw,xx=0.
In this case when we discretize the equation using Galerkin's approach, the damping matrix becomes diagonal with every element same for standard boundary conditions.
It is better to answer your question from the assessment.of free vibration of a sdof system governed by the ode
MUtt  + CUt + KU =0                                                                                        The solution to this equation is   U(t) = A*exp(-ωdt)Sin(ωdt +α)                                   where  ωd = ωn*sqrt(1-D2)   and ωn = circular natural frequency and D is the damping ratio = C/Cc.   The decay factor is exp(-ωdt).   The higher the frequency the faster the decay and the more the damping. Thus, the decay rate will vary with frequency.  As is well known the viscous damping coefficient for a sdof system  is defined by                             c = 2DMωn                                                                This idea can be extended to strings and beams.
I hope this answer will be useful to you.
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Why bending stiffness and torsional stiffness of the interface rings should be same in a marman clamp band system
There are various ways to formulate stiffness, but we can skip that and go straight to the explanation.
Lets define up to be in an axial direction. We apply a torsional moment to all radial cross sections, for example as an upwards force acting on the outer lower corner, balanced by a pressure on the upper edge. This leads to a small and equal rotation of all these cross sections.
The upmost part of the cross sections move inwards. The lower parts move outwards.
Now lets slice a tangential, curved plane, cut at any radius  R you like.  All parts are 2piR horizontally. The upper part used to be on a larger radius. The upper part of our ring has just become shorter than it was. The lower part has just become longer than it was. The centre though has stayed on radius R and is just as long as it were. Its a little sheared though.
Sounds familiar? This is the same strain deformation as in bending.
I would not call this torsion, my own mother language has more precise terms. Perhaps someone with better language knowledge could come up with the right term? Wringing?
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Hi
I am working on mitigating traffic induced vibrations on buildings. I am looking for measures that can be applied at the RECEIVER side to mitigate vibrations. I did some research and I could find measures such as Free/ constrained layer damping, tuned vibration dampers, changing mass/ stiffness of the structure, base isolation. Can somebody suggest more measures that are practical?
Thanks
I also agree with Claes.
Moreover, there is also the option of isolate the entire building using viscodampers in the link between the building and its foundation. We have applied this technology in a building in Barcelona for the isolation against underground traffic and the results are satisfactory.
Tuned mass dampers is something in which we are working on in our research center. But, since they are only interesting when the vibration signal is close to be tonal (very well defined peaks in the vibration frequency spectrum), I think that they aren't a good general solution for your problem.
Bests,
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Show me your model you will use, plz.
Thank you for your answer and publication you have recommended, I just wonder which kind of model she will use in pulsatile flow research for crossflow.
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Because I could only use the compression type accelerometer which is more sensitive to the zero shift in the impact test, I cannot obtain the accurate signal, and thus cannot obtain the correct velocity, displacement using common integration approach as well. The velocity and displacement shows unrealistic trend to increase continuously without approaching zero.
So my problem is how to process the acceleration correctly with matlab (preferred) or any other software, the detrend function in matlab seems to be unable to handle this problem.
After reading several relevant literatures I found that the discrete wavelet transform (DWT) method and the empirical mode decomposition (EMD) method may be appropriate to be applied. Have you ever met similar problem during the impact tests? Looking forward to hearing your experiences and thanks in advance.
The brief introduction is enclosed as attachment.
Hi
This is a classic problem & a nuisance.
Try these steps.
1. Select a time record with zero offset at start and zero offset  at end.
2. If you do not have such a record, apply exponential weighting to get zero offset at the end.
3. You should now have a saw tooth pulse of duration tau seconds and hence, 90% of its energy below 2/tau Hz.
4. Take a FFT of the whole signal.
5. Delete any spectral components below 2/tau Hz.
6. Apply integration using jw as appropriate.
7. Take a FFT of the whole signal to return to the time domain.
8. Plot the signal.
The FFT is cyclic so, doing 2x FFTs in a row only returns your original time signal - try it. Note that you need long time records for the approach to work at least so so.
The above can be done in Matlab.
A better way, if you can repeat your test, is to use mechanical filters to remove the high frequency content that upsets the sensor. Take a look here.
/Claes
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I performed modal analysis of a plate fixed on both ends. I extracted five mode shapes. How can I decide the frequency range for harmonic analysis from modal analysis. The details of my analysis was attached as image.
I think can explain the phrase "frequency range based on the loads that are relevant in your application" with another example:
Assume a three storied building with an electricity generator (gen-set) at the top. We know the RPM and the force generated (from the manufacturer's spec). We can analyse the FE model for obtaining the eigen frequencies. Then the most important eigen modes are those having frequencies within the gen-set's operating frequency plus or minus 20%. So consider all modes from lowest to the gen-set's operating frequency plus 20%.
Hope I haven't missed anything important connected with the procedure.
regards,
Rahul Leslie
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I would like to simulate ambient vibration in a numerical model such as a MDOF shear building. In some cases, the use of random Gaussian white noise can be a solution. Is it a plausible approach?
Thank you
Moreover, you can simulate the ambient vibration caused by wind in your numerical models. For this goal, you need to introduce with aerodynamic forces such as self-excited forces and buffeting forces in wind-induced ambient vibration simulation. Although these forces are usually dominated in bridges. The following reference may be useful:
He, X., Moaveni, B., Conte, J.P., Elgamal, A., Masri, S.F., (2008). "Modal Identification Study of Vincent Thomas Bridge Using Simulated Wind‐Induced Ambient Vibration Data." Computer‐Aided Civil and Infrastructure Engineering 23(5): 373-388.
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I need to fit a damping sinusoid model to a given data (i.e. estimate amplitude, phase, damping factors). I need it to be applicable to multiple sinusoidal models too. any suggested methods?
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find acceleration and velocity in harmonic analysis in ANSYS APDL?
Very Good tutorials for Finite Element Simulations with ANSYS Workbench 17
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Hello,
I have condensed a Finite element model from 8 nodes with 6 dof at each node into 2 nodes with 6 dof at each node using a static condensation method (or Guyan reduction). Now i would like to translate this nodal data (represented in stiffness matrix) into a 3D beam element. So for that i need the beam element properties (like Moment of inertia (Iyy and Izz), Polar moment of inertia (J), Shear modulus (G), Young's Modulus (E), Cross sectional Area and length (L)) from the 12 by 12 stiffness matrix.
What makes it difficult is that the model which i have reduced is made of different material at each sides hence the model does not have a constant Young's Modulus (E) or shear modulus (G).
Can anyone help me in finding out the beam element properties using the beam element stiffness matrix? Well we all know how to do the opposite.
The 3D beam element stiffness matrix definition and Finite element model descriptions are given in the attached .doc. The finite element model shown in figure 1 is before condensation, then the model is condensed into 2 nodes and the condensed stiffness matrix is given by Table 1.
Any help will be appreciated.
Thank You,
Paul Thomas
You can try the general-purpose multiscale constitutive modeling which can take a block of material and homogenization it to a beam. The code can be freely launched in the cloud at https://cdmhub.org/resources/scstandard
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After analysis, I want to determined mode shape vectors for linearly elastic vibration modes. PERFORM 3D is announced "There are no Modal Analysis load case in this analysis series". How do you define Modal Analysis load case in PERFORM 3D and export result?
Best regard
Dear Dieu,
If the load case type is based on mode shapes, specify the pushover
direction, the modes to be used, a scale factor for each mode,
and a base shear direction for each mode.
Use the Add, Insert, Replace and Delete buttons in
the usual way to build up a modal load list. Only horizontal
translational masses are considered for push-over loads. Vertical
translational masses are ignored, and rotational masses do not
Symmetrical Structure
If you choose loads based on mode shapes, and if you use more than
one mode shape, you must specify a scale factor for each mode. Only
the relative values of the scale factors are important, since the concern
is the load distribution over the building height, not the load magnitude.
Consider first the case of a symmetrical 3D structure with mode shapes
that are clearly oriented along the H1 and H2 directions. The following
procedure is suggested.
(1) Get the mode shapes and periods. This usually means that you
must run an analysis to calculate the periods before you can define
(2) Examine the mode shapes and determine, for each of the H1 and
H2 directions, which is the "first" mode and which is the "second"
mode. For example, modes 1 and 4 might be the first and second
H1 modes, and modes 2 and 5 might be the first and second H2
modes. You may also consider the "third" modes. Ignore torsional
modes.
(3) Choose a design response spectrum. This is a separate task, and
you can not do it in PERFORM-3D. Only the shape of the
spectrum is important, not the intensity.
(4) For each mode, get the mode period and hence get the spectral
acceleration from the response spectrum. This is the scale factor
for the mode.
(5) Decide on a push-over direction, say H2. Specify the angle to this
direction (= 90 degrees for H2).
Chapter 13. Static Push-Over Load Cases
PERFORM-3D User Guide 13-9
(6) Specify the mode number for the "first" mode in the push-over
direction (= 2) and the scale factor for this mode from Step (4).
Choose "+D" for the base shear direction. Since the structure in
this example is symmetrical, the results will be the same for +D
and –D push-over.
(7) Specify the mode number for the "second" mode in the push-over
direction (= 5) and the scale factor for this mode from Step (4). If
you want the base shears for modes 1 and 2 to be in the same
direction choose "+D" for the direction, else choose "-D".
(8) If you wish, repeat Step(7) for the "third" mode.
You may ask why it is necessary to specify the angle to the push-over
direction. For the symmetrical structure in this example, PERFORM-
3D could figure out the direction, since both mode 1 and mode 2 have
base shears only along H2. Also, since the structure is symmetrical it is
necessary to consider push-over only in the +H2 direction. In general,
however, it is not that simple.
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Just as the question.
I've got a detailed and systematical introduction on numerical model of the soil-pile intercation on a sesimic load in the dissertation from the attached link. In figure 3.11 and 3.22 (the atteach picture), page 72, it is reported that real part of the impedance function is obtained from FEA,here Abaqus.
But anyone can tell me how to work it out?
can the analysis be implemented in universal step?
Is this method suitable to a harmonic load uniformly acted at the pile top?
actually, it is dynamic stiffness. Kd=F(w)/U(w)，w  denotes frequency
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I was simulating the response of a two DoF system with a constant frequency force acting on the second mass. The system was initially at rest. The response obtained through simulation shows that the structure vibrates at three frequencies, the two natural frequencies and the forcing frequency. However the two natural frequencies appear only in the initial part of the response. The system consists of two masses, three springs (one connecting the masses), and two linear viscous dampers. System is fixed on both the sides.
Your results seem plausible. The system oscillates in all 3 frequencies. Due to damping, the oscillations in the eigenfrequencies will vanish quickly, leaving only the steady-state response of constant amplitude in the forcing frequency. Without damping, you should always see a superposition of all 3 frequencies.
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is it possible to represent a flexible body by a multiple of rigide bodies (>10 bodies), this rigide bodies are attached between them by springs and dumpers so they can behave exacly like the flexible body once they are excited at the eigen frequencies of the flexible body. i know some will say try to mesh it, but i don't have a good FEA soft, so i'm trying to represente the meshed body in a non Finite element software.
thanks
Eigen frequencies and modes are dependent on the stiffness and mass interaction between nodes. As you know, for a given mesh and no. of eigenvalues requested during extraction, you've only certain no of eigenvalues accurate (this is due to eigensolving technique).
Mass distribution is easy, as many codes utilize lumped mass system.
Stiffness distribution will be tricky as depending upon type of elements, each node will have certain no of stiffness components. So theoretically it's possible to retain in rigid body system with springs, but practically it'll be quite difficult. Just look at stiffness matrix of a simple spring. Each node interacts with the other node (off diagonal terms in stiffness matrix). Similarly in a beam element, each dof will interact with other dof of the same node + the node at the other end. Simple springs generate uncoupled stiffness matrix. If you know a way to account of inter dof interaction, then yes you can do what you want, otherwise no :)
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I'm proposing an upgrade in a Mechanical Vibrations Lab, where some basic experiments will take place. So I'm collecting suggestions of equipment or instruments that could be applied in this lab.
Some of the experiments are listed below:
-Free vibration of spring-mass system
-Free vibration of a cantilever beam
-Bump Test
-Signal processing
-Logarithmic decrement estimation for a cantilever beam
-Free vibration of a damped, single degree of freedom, linear spring mass system
-Forced vibration of a cantilever beam
-Free vibration of a two-DOF system
-Unbalance response of a rotor-bearing system
-Vibration isolation
-Bearing fault diagnostics by FFT analysis
-Acoustic experiments
Dear Sir,
I have been through this lately in my institution. I hope you'll find this list helpful:
1- Vibration analyzer (may be B&K PULSE system if the budget allows) or NI-CDAQ or CRIO for data acquisition together with Labview software and NI Sound and Vibration assistant which is a very powerful tool;
2- Vibration exciter with its power amplifier and signal generator or exciter control;
3- Accelerometers (different sizes to suit different applications); a triaxial accelerometer will be an asset; magnets and wax for mounting;
4- Hammer;
5- Force transducer;
6- Tachometer;
7- Proximity transducers;8- Conditioning amplifier.
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Rotating bladed disk is modeled as a coupled spring mass system. The spring mass system is represented as 2nd order non homogeneous system of ODEs with time varying oscillating coefficient where stiffness matrix is having a banded structure containing sinusoidal terms. I know for constant stiffness matrix, Newmarks time integration scheme gives stable results. But I wish to know how analytically and numerically time varying stiffness can be handled.
This is really no different than a nonlinear rotor dynamics problem, and Guyan reduction is extremely effective in removing higher order frequencies that push the time step to extremely small values.
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I am looking for a good software to be able to simulate ultrasonic vibrations in glasses. The amplitude of vibrations is in micrometer scale and I'm not sure whether FEM is the right way to deal with this problem or not.
Hello Masoud,
Best regards
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Suppose a 6 story linear building structure with known M,C and K matrices. How is it possible to transfer it to a nonlinear building by adding nonlinear stiffness force calculated by Bouc-Wen model to every story?
Yes, there are several non-linear identification methods. I've dealt with the problem for a 2DoF system in the paper that I attach to the answer. You can think also about using an Unscented Kalman Filter, but for a 6DoF system (assuming you consider it having shear-type behaviour) the state-space formulation is quite tedious. For UKF I suggest to refer to the work of E. Chatzi and A. Smyth.
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How does one accurately measure the effective dynamic load exerted by heavy equipment (huge vacuum pump, multistage centrifugal pump, etc) trasmitted to arbitrary floor without reallocating the equipment?
One method I can think of is to work out the FRF of the floor at a point close to equipment foundation with a force hammer when the equipment is in rest and capture the floor response when the machine is operating. The dynamic load can be then be determined by the relationship of input and out. According to theory it should work for cases with single-toned harmonic excitation, however the equipment is expected to emit multi-toned or non-harmonic excitation.
Is there any other method in dealing with this kind of  problem?
It seems trivial, but it is not. You can proceed measuring the global response with an accelerometer but you have a very large error near the resonances of the structure supporting the machine. That's why in modal testing you typically use a load cell where the shaker is in contact with the tested specimen: in order to clearly measure the real force. You can check on Ewins book "Modal Testing", it describes in detail the problem of measuring the real force between to moving object.
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I am doing study of stone blocks using impulse response (hitting by hammer at one point and collecting acceleration signal at other point by accelerometer, i.e. impulse response). While going through literature and response plot, I have few questions and looking for guidance: I am looking answer with respect to peaks amplitude and its locations of impulse response frequency plot which has multiple peaks in it.
1. Do these peaks are at natural, damped or resonance frequencies? (all systems have some damping).
2. What is importance of dominant peaks compared to others in a same spectrum?
3. Why do we get some higher peaks compared to others?
4. What will be impact on these peaks' frequency when there is crack between hit and sensing point on same stone block compared to non-cracked pair of hit and sense point, i.e. does peak frequencies will shift to lower or upper side of spectrum or keep old peaks as well introduce new frequencies in spectrum or other way, dominant frequencies will change?
5. Similarly, when material is soft between hit and sense point?
6. Does crack introduce new degree of freedom, i.e. new peak frequencies?
My assumption as per theory, crack reduces the stiffness of material, porosity changes stiffness, mass(density) and increase damping.
Hi
What Prof. Khulief writes is all true.
A small boat floats on top of the wave while a large boat drives through the wave, i.e. size versus wavelength greatly matters.
However, there are a few things more that goof things up for us. These have been known in the field of acoustics from experiments since the late 1920's and its theory was developed by M Schröder in the 1950's.
There is something called called the acoustic limit, or the Schröder limit.
Here it goes.
The asymptotic solutions to implies the modal count for a room implies that the number of modes, N, grow with frequency, f, as f3 for a volume. At high frequency, i.e. at a frequency where the wavelength is short in comparison with the dimensions of the volume, there will be a high number of modes as counted per Hertz.
The modal density, n, is the average mode-to-mode separation.
The half power bandwidth, dfj,  of a mode, j, is dfj = eta/fj , where eta is the damping loss factor.
Now, at high frequency, the half power bandwith will grow with frequency while the modal density will shrink.
Schröder showed that when three modes fall inside the half power bandwidth of a single mode, then a FRF will have random phase and one stadard deviation for the FRF amplitude is 5 dB to 6 dB, i.e. with about 90% confidence, the FRF amplitude variation is in the ballpark +/- 10 dB.
Incidentally, this is the criterion also for diffuse field conditions provided eta is moderate.
The kicker is that when passing through resonance, the FRF phase jumps 180 degrees. Add a tiny bit of uncertainty to the resonance frequency and start summing modes and you will readily see what happens.
The FRF dispersion has been demonstrated through carefully made tests on production sets of nominally identical cars by various people in the 1990's when FRF measurement became easier to do. It had been shown for other product types long before this.
The mode separation, modal bandwidth relation is called Modal Overlap, where MO = n*eta/fj . MO = 3 at the Schröder limits.
Reliable damping estimation uses some sort of modal algorithm for identification. Such algorithms tend to work up to MO <= 0.3. Sure, you can apply them at higher MO but you get unique results every time, i.e. tweak your assumptions just a tiny bit (e.g. the selected frequency range or vary algorithm parameters) and the mode set you identify will be a new set and so on.
I enclose a presentation on this matter that was made by two of my former colleagues, B Gärdhagen and J. Plunt, which demonstrates the above and shows why people working with acoustics do things like sum energy (a squared quantity) and work with power based concepts.
At high frequency, it turns out that FRFs disperse while energy/power converges.
To summarize, for high observability, you must for small cracks go up to high frequency - where you may struggle with the Schröder limit. For large cracks, you may use FRFs at low frequency.  Note that the modal density function varies with object form, the modal count is very much different between volumes, plates and beams. Therefore, you may have more success for certain object shapes.
I do not mean to depress you but the above is old, hard won, knowledge that repeatedly has been proven.
Hope this helps
Claes
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There is a structure with n degrees of freedom.The structure has forced vibration by cyclic loading. The loading period and its values depends on a parameter. in Ansys workbench how can found this parameter values cause resonance?
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Hi everybody,
I'm going to do dynamic analysis of a vibrating string in ABAQUS. The string is vibrating at a specific frequency and at time t1 boundary conditions are altered in such a way that tension is released while the string is still vibrating. How to model it in ABAQUS?
I'm using Static (General), Frequency and finally Modal Dynamic steps in succession. In the Modal Dynamic step, while the string is vibrating, tension is released by returning the boundary displacements to the zero point.
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When i solve an eigenvalues and eigenvectors (or frequencies and mode shapes) problem of a multiply degrees of free system. I found frequencies of the system: omega1, ơega2, omega3,....,omega n and corresponding to mode shapes. And, you know that, if structures are excited at what frequency then it will oscillate with corresponding to mode shape. And here, I assumed that, the structure is excited at a frequency range between omega 1 and omega 2 (or any range, such as omega 2 - omega 3, and so on). So, How the structure will oscillate with what mode shape?
Hi
Your question is a class room question, but a good class room question that is worth delving on.
The simplest way to undrestand this is to look at the swing, i.e. an item most of us have an in-depth study from when we were kids,
The swing is a pendulum, i.e. its resonance is w = sqrt(g/L), where g is 9.82 m/s2 where I live and L is the pendulum length. This provides the same resonance frequency irrespective of passenger weight.
If you push the swing, you can do so at any freqyency. For simpicity, let us assume that you move the swing slowly at large stroke at a frequency much lower than w. This is not easy when the passenger is heavy as, in essence, you then must lift the passnger. The same applies if you try to push the swing much faster than w, only in this case, it is the passnger inertia that resist fast oscillation.
In both cases, as soon as you stop the forced excitation, the swing will use whatever kinetic and potential is avialble and distribute it into its most favorable setting, which is a split where all kinetic energy can shift to potential energy and vice versa, which can be achieved only at its natural frequency, w.
The reason why it is easier to push the swing at w is that it then stores energy when excited at resonance. Free vibration implies vibration at natural frequency.
If we take a mass spring system. Potential energy is 1/2*K*X^2, where K is spring stiffness and X is displacement. Kinetic energy is 1/2*M*V^2. For harmonic vibration X = A*e^jwt, we find that V = jw*A*e^jwt = jw*X.
Inputting and summing kinetic energy, we find that
1/2*K*X^2 + 1/2*M*(jw)^2 = 0
solving whis equation produces the natural frequency w = sqrt(K/M), which just is another way of stating the energy summation listed above .
Multidof really is the same thing with information added as to where you drive and how this matches the mode shape.
However, to better understand things, take a look here
For modal summation, I enclose part of a course I hold now & then on structure vibration which intended for an audience without prior knowledge on vibration. This excerpt treats a lumped 2dof system and explains most of what you are asking for.
Have fun
Claes
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I'm trying to find a review of there methods
The most common methods are subspace iteration and Lanzcos method. You will find further details in the books by Louis Komzsik What every engineer should know about computational techniques of finite element analysis and Klaus-Jürgen Bathe's Finite Element Procedures.
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By keeping I marker fixed the J marker has displacement and also small rotation. How to manually calculate the result of Spring force with reference to ADAMS. ?
Let us assume linear spring .
This gives value in 1D. But I have displacement in 3D space.
For Ex. To calculate total force/reaction by the spring/suspension between chassis and wheel carrier
Note: any axis of I marker at chassis and J marker on wheel carrier are not parallel.
I really appreciate any ones advice and suggestions.
Thank You.
I thin by measuring the absolute distance between to markers, you can calculate delta_X, and ........
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In finite element, I have a cantilever beam (system level) consisting of components A and B joined together (as shown in the figure below). I applied a force of 1N at the free end of the cantilever and I got the x- and y-displacement of each node. Now, I want to isolate component A (component level) and apply boundary conditions to it. My goal is to achieve similar x- and y displacement on each of the nodes of component A, both at the system level and component level. How can I go about it? What boundary condition(s) can I apply to component A only in order to achieve the similar nodal displacements I had when components A and B are combined? I am working in MATLAB.
Thank you.
Best compensation for B component impact on A component would be forces applied by B on A on each node. Maybe you could try to analyze component B by itself to get reactions in nodes which are common for component A and B, and then that reactions apply on nodes on component A as loads. It would not be exact the same nodal displacement of A, but you could try.
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Dear All
I am trying to include tuned mass dampers in footbridges. Someone who recommend me how can I calculate the properties for tuned mass dampers in footbridges to minimize the acceleration keeping the TMD relative displacement.
Thanks a lot
Best regards,
Nati
Hi Nati,
you might be interested in a paper by Krenk and Hogsberg
"Tuned mass absorber on a flexible structure", Journal of Sound and Vibration, Vol. 333 (2014) pp. 1577--1595.
Best regards,
Nils
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Dear researchers;
I need to build a state space model for a three storey building in Simulink MATLAB: the equation of motion of the building is given by:
Mx'' + Cx' + Kx = Tf - MAx''g
The building is equipped with a damper that produces a force represented by (f).
Hi Mahdi,
I am recently studying on the same subject with you. It is hard to visualize and understand all system. Sometimes I have problem with that. Can you please check out  word file that attached in the post? I hope this help you.
Best regards,
Osman
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Goodmorning. I'm trying to model a simply supported beam subjected to a moving sprung mass, as illustrated in Figure 1. Basically, I've modeled the sprung mass as a reference point with a mass of Mv. I've created a reference point as the point where there is going to be the interaction between the sprung mass and the beam. The “Node to Surface Contact” feature of ABAQUS was used to simulate the sliding motion on the frictionless surface of the beam.
I have then created two steps: in the first step the gravity is introduced and in the second step a dynamic analysis is introduced (the sprung mass moves from 0 to L).
Now, the model works but I have a totally bad result. In particular, I don't want that the gravity load is applied also to the beam, I've tried to apply it only to the reference point where the mass is applied but it is not possible. Is there a way to, after the first step (where the gravity is applied to the whole model) to bring the beam at the original position?
I have attached the script of my model if it is needed.
Thanks for any help.
Kind regards
I have tried different solutions but I still do not have reached the correct one. Here is what I have done:
1. Dynamic analysis considering, instead of a point mass with gravity an equivalent concentrated force (but not considering the gravity applied to the beam)
2. Dynamic analysis considering, instead of a point mass with gravity an equivalent concentrated force (considering the gravity applied to the beam)
3. Dynamic analysis considering a point mass with gravity and the gravity applied to the beam
No one of this model works as I aspect. As I have seen in previous works the ABAQUS model should be exactly as the exact solution (see attached image :BLUE line).
What do you think could be the problem?
I take this opportunity to wish you merry Christmas.
Best regards
Giacomo
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I have done the experiment on a RCC bridge scale modal in laboratory , from that got the natural frquncy as 100Hz, but when im doing the modal analys in ANSYS APDL which value need to consider the naturla frequncy(like if 12 modes are there 12 frequncies will be there)
ANSYS APDL uses FEM platform. Through FEM analysis we get conjugate pairs of natural frequency. like if we take example of a beam we can get 23.5Hz for first mode and 23.3 hz for second mode, these two are mode shapes of a beam but however one may be bending and another may be torsional. Similarly we can get bending modes in different planes. To understand this you will have to study the theory behind the modal analysis using FEM. "DYNAMICS OF ROTATING MACHINES" book provides an easy and good understanding about conjugate pairs.
In experiment like yours the mode which you get depends on the placement of sensor and direction in which it is measuring the signal. So, through software take that mode which gives the displacement in the same plane as you are getting from experiment.
I hope I am able to explain it.
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Hello all,
I am simulating single-mode dynamics (but in various modes) of a micro-beam with modal damping ratios of about 0.001 in Abaqus/standard. The question I have is why Abaqus does not have a simple viscous damping model (zeta) like as what we learn in theory of vibration?
Are there any alternative method of entering modal damping ratios other than calculating coefficients of alpha and beta in Rayleigh damping?
Thank you,
*MODAL DAMPING
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In order to validate a new algorithm, I need reliable reference solutions of the dispersion curves of coupled elastic/fluid acoustic waveguides. These could be either fluid-filled pipes or layered plate-like structures involving fluid layers.
I am looking for either a publication that presents dispersion curves (and gives all relevant parameters that allow reproducing the results) or software (I am using 'disperse' but am not sure the results are correct.)
I would appreciate if someone can point out other sources.
Dear Hauke,
in addition to the references mentioned by Huangchao Yu, you may also want to have a look at these publications, if you are interested in wavelengths much larger than the tube radius:
Solution for thick-walled elastic pipes with infinitely high Young's modulus (two modes, one shear-dominated, one fluid-dominated):
Bernab ́e, Y. (2009a), “Oscillating flow of a compressible fluid through deformable pipes and pipe networks: Wave propagation phenomena”, in S. Vinciguerra and Y. Bernab ́e, eds, Rock Physics and Natural Hazards, Pageoph Topical Volumes, Birkhäuser Basel, 969–994
Solution for thin-walled elastic pipes (solid acts like an elastic shell, dissipation is captured phenomenologically):
Gautier, F., Gilbert, J., Dalmont, J.-P. and Vila, R. P. (2007), “Wave propagation in a
fluid filled rubber tube: Theoretical and experimental results for Korteweg’s wave”, Acta Acustica united with Acustica 93, 333–344.
Literature Review from 1975 with figures of dispersion relations:
Tijdeman, H. (1975), “On the propagation of sound waves in cylindrical tubes”, J. Sound Vib. 39(1), 1–33.
The limit-case for a rigid solid (fluid wave only) can be found in works of Biot and Womersley:
Biot, M. A. (1956b), “Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher-frequency range”, J. Acoust. Soc. Am. 28, 179–191.
Womersley, J. R. (1955), “XXIV. Oscillatory motion of a viscous liquid in a thin-walled elastic tube-I: The linear approximation for long waves”, Philos. Mag. Series 7 46, 199–221.
Analytical solutions are difficult to derive for non-trivial cases as the differential equations easily get very complex and require numerical methods, e.g:
Bansevicius, R. and Kargaudas, V. (2005a), “Wave propagation in elastic cylindrical tubeswith viscous and heat-conducting fluid”, Ultragarsas 3(56), 7–10.
Bansevicius, R. and Kargaudas, V. (2005b), “Wave propagation in elastic cylindrical tubes with viscous and heat-conducting fluid”, Ultragarsas 3(56), 11–16.
Best regards
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1. For study of  vibration of cylindrical shell i need to find Governing equation by using energy function with Ritz method.
2. Use of Hooks law ,strain vectors ,resultant force and moment relation and strain energy and kinetic energy find the equation for frequency.
Hi
Here are good classic references for plates and shells
Leissa - Vibration of plates: http://ntrs.nasa.gov/search.jsp?R=19700009156
Leissa - Vibration of shells: http://ntrs.nasa.gov/search.jsp?R=19730018197
I believe that you find what you are looking for in the Leissa books.
Sincerely
Claes
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