Structural Dynamics - Science topic

Hi Braj,

Where did you come by this statement? If we would be considering a free structure, the first two modes would be rigid body modes and thus, would tell you little about dynamics.

Hence, the dynamic behaviour of a structure can in general not be understood by known the first two eigenvectors/mode shapes. It highly depends on the excitation of the structure, i.e., which frequency range is contained in the exciting signal. Therefore, there is no general rule on how many modes are sufficient. This must be judged on a case by case basis.

To find out which modes are dominant in a certain transient deformation case, you can compute the modal participation factors. But to do this you must have an idea of the real deformation that will arise under operational conditions.

This is definitely a topic you can discuss in more details with Elmar Woschke

and his group.

Cheers,

Sascha

The modes shapes of a system are orthogonal to each other but with respect to mass and stiffness matrix of the system. Therefore, they are not directly orthogonal to each other. MAC or other approaches do not determine whether the modes are independent from each other. They only give how close the one vector (mode shape vector) to another vector (mode shape vector). MAC value clsoe to 1 means that they the two vectors (in this case modes) are very close to each other; hence, they can be treated as the same modes. MAC value close to 0 means that they are different modes. Therefore, these approaches are used to identify whether a mode obtained from two different approaches (two different programs, analytical versus experimental, etc.) are the same modes or not. However, they do not give any idea about whether the mode shapes are orthogonal or not, since orthogonality is defined based on the mass and stiffness matrices of the system.

There two things to be considered for the determination of which modes will participate in the response.

1) First is the frequency range of the excitation acting on the system. Neglecting the damping the system consider the 1/(wr^2-w^2) term for each mode r for the frequency range of interest. You can eliminate the modes which have very small values (use threshold value) from your solution.

2) Second is the forcing itself. Where it is applied and which modes it can excite. You can simply calculate the modal forcing term i.e. Phi_r^T*F as if the force is constant. Eliminate the modes selected based on the first criteria if modal forcing is very small (use threshold value). Then use the remaining modes in your analysis.

If you want, you can combine them to get a simple expression.

Hello Mehdi, I encounter the same question, my acceleration is greater than 10 times than seismic acceleration. Did you solve this problem ?

If you solve, Can you give some suggestion to me? Really appreciate you.

Best regards,

For your specific project, you'll need to do some research to determine the best method of coding and programming in order to finish the analysis of the cantilever composite plate. The method of finite element analysis (FEA) is often used to model and solve complex engineering problems such as those involving the analysis of complex fluid dynamics. FEA allows for a highly accurate approximation of physical problems based on discretization and numerical integration of the equations of motions. Some popular software packages for FEA application are MSC Patran for the modeling language, Hawk-I for the computational engine, and Abaqus for the post-processing tasks. You can then look up tutorials online that provide step-by-step guidance on how to code a finite element analysis (FEA) of a cantilever composite plate. Most examples will involve employing a computational grid to discretize the problem into elements with associated properties, using a stiffness matrix to relate force and displacement, and expressing the equations of motion in terms of a numerical integration. Once you've completed the FEA analysis of the cantilever composite plate, you can then turn your attention to the next step of flutter analysis. Flutter occurs when an aerodynamic force causes a structure to become dynamically unstable. The process of flutter analysis involves using post-processors such as ABAQUS to analyze the data from the FEA procedures and to calculate the critical speed at which the structure can become unstable. I hope this information has been of help to you and good luck with your project!

Thank you Pavlo Pavliuchenko sir for this insightful answer. This does clarify a lot of things. Of course, covid induced restrictions did play a huge role in limiting us from going out to search for experimental data or real-world data that we could have used for our FE model. However, we can surely find some literature to validate the results. Thanks

Since you've mentioned all natural frequencies are zero it also important to know how many modes are extracted from Ansys?

If you have multiple bodies which are not constrained, each one will add rigid body modes (RBMs) to the problem, and you will end up with many zero frequencies. For instance, with no constraints a body in 3D will have 6 RBMs. If you have 2 such bodies, you will have 12 zero very close to zero natural frequencies.

You can plot the mode shapes that have zero natural frequency to visualize if any of them is not constrained properly and moving freely with respect to other parts. Exaggerate the mode shapes to observe the motion better. If this is the case, you need to define the boundary conditions properly. This might be due to the improper definition of contact surfaces in Workbench. If that is the case, you need to bond such surface to each other.

The f0 can be estimated from the deflection: 16/(3,6)^0,5 = 8,4 Hz. There are probably more resonance freqencies, as there are several supports. Rocking, swing etc. However the first vertical mode is the one we look at here.

For the transmission loss you can look for the classsic viscoelastic transfer function using the above f0 and 3% loss factor.

Dear Muhammad Ichsan

Nice and important question and nice answers. As a maybe late comment (probably you already do not need the answer), there is legalized comment on the integration step in the seismic standard of New Zealand; see the references below:

[1] NZS 1170.5 Supp 1. Structural Design Actions - Part 5: Earthquake Actions. Standards New-Zealand, New Zealand, 2004.

[2] NZS 1170. Structural Design Actions, Part 5: Earthquake Actions-New Zealand. New Zealand, 2004.

according to which the digitization step of the earthquake acceleration is an upper-bound of the time integration step. Still, there are techniques and methods suggested for using integration steps larger than the earthquakes steps. I have recently presented a review on one of them, where you can also see explanations about the others. The reference, also attached, is

A. Soroushian. A technique for time integration with steps larger than the excitation steps: Review of the past addressing the existing challenges and a perspective of the future. In Proceedings of 8th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN2021), Athens, Greece, June 28-30, 2021.

In any way, as also implied in the response of dear Iolanda-Gabriela Craifaleanu , according to reference such as the Structural Dynamics book of Clough and Penzien 1993 and even main references from numerical solution of initial value problems, for the sake of responses sufficient accuracy, the time integration analysis need to be repeated with smaller steps once or by times . . . .

OK. many sincere thanks for your kind attention, and best wishes for all of the people in this question group especially regarding health and happiness . . . . . .

Dear Mahdi,

Greetings.

Buc-Wen is usually being used to model base-isolated systems. The model has been employed for so long, indicating its high accuracy in predicting the nonlinear behavior of such systems. However, the issue is that such a model requires solving differential equations (numerically) to estimate the modeling parameters, which sometimes requires rigorous efforts.

There is an alternative to that material. The algebraic material existing in OpenSees (https://opensees.github.io/OpenSeesDocumentation/user/manual/material/uniaxialMaterials/HystereticPoly.html) is a new type of material that brilliantly overcome such a shortcoming and matches to existing experimental tests.

The related resources are:

1-

2-

There is also a MATLAB program (ParIde) developed by the authors that can help you estimate the modeling parameters. The model is numerically accurate since I have tested it against multiple loading protocols.

BR.

Following

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.

The application of jerk in physics have many instances and one of the example I can shot is simple that the jerk is nothing but it is all about the rate at which any objects acceleration changes with the time or with respect to time.

Dear Mehran Shahpari

First you should find the mass matrix and the stiffness matrix. Afterwards, you should solve the eigenvalue problem associated with the problem at hand and these specific matrices. The structural damping coefficient is equivalent to the fraction of Im(lambda) over Real(lambda), where lambda is the complex eigenvalue and Im and real, respectively denote imaginary part and real part of the eigenvalue. I have attached a triple of screenshots to my comment for your perusal.

For forced vibration (for example in presence of air dynamic pressure), the solution of the eigenvalue problem is a bit harder than to find a solution to an ordinary eigenvalue problem. For concreteness, in this regard, I have attached a PDF of my own original idea to this comment. The PDF is also available in my ResearchGate project:

Linear Aeroelastic Analysis of Laminated Composite Plates with Fully Elastic Boundaries

Under the title:

Eigenvalue problem for aeroelastic vibrations: The solution

yes, your diagnosis seems correct since the difference is of order of 1e-8. in computers, no floating point number can be represented exactly. therefore, it's common to use some epsilon value is used to avoid it. alternatively, when writing from scratch, only upper or lower diagonal is saved in the memory for a symmetric array to avoid such issues.

Dear Ali,

the maximum response recorded by your accelerometers is mathematically the CONVOLUTION of the structural response of the bridge (with a peak expected at each natural frequency) and the excitation by the trucks (with a peak at their own suspension frequency) meaning the frequency of the maximum response is a mix of both! Of course the truck's primary suspension frequencies vary from a truck to the next, still in the same range.

In addition the natural frequency of the bridge is load dependant (weight and position of the heavy trucks at the time of the record), and temperature-dependant (meaning day/night, clear day/cloudy and seasonal fluctuations...)

Back to your precise question, you have just NO WAY to determine the exact bridge natural frequencies by this "natural response" method. As suggested, you must close the bridge (however with the same added load than the usual traffic) and use for example a dropped weight to generate a broadband shock (preferably located in consideration of the anticipated mode shape, which allows you to trigger distinctively the first flexural/torsional modes). And still the exact frequency will vary with the previously mentioned load and temperature conditions... Sorry for you, that's just the complexity of structural vibration physics!

Back to Vahid's remark, we could only appreciate the likely natural frequency range of your bridge by knowing its precise construction and span, but the natural frequency of very long bridge spans can even be below 1Hz (remember the ill-fated Tacoma bridge, destroyed by wind gusts at approx. 0.5Hz resonance https://www.youtube.com/watch?v=j-zczJXSxnw). Obviously short bridges have higher natural frequencies but you can interpret it as revealing over-designed structures! The Tacoma bridge example is also a good evidence of the 3D complexity of the mode shapes (something also well evidenced by Eric's study, which provide a very accurate in-situ modal analysis). My guess is that in your case the 2.6 to 3.1 band correspond effectively to the interaction of the trucks suspensions with one of the main natural frequencies of this bridge... in this global 2.8 +/- 0.3Hz band! But don't ask for more precision...

WWER - water-water energetic reactor

Dear Aichouche

If I were you, I would forget the Castem and go for SolidWorks Simulation . it's more easier, faster, and efficient.

There are two ways-

1. Spectral simulation method- Find output spectral density (So) using harmonic transfer function and input (force) spectral density (Sf). Then calculate the required mean square response (MS) from the area under Sf curve over required frequency band using the numerical integration of Sf function.

2. Time domain method- First you are required to generate the time-domain force f(t) signal using ‘wgn’ function in the MATLAB and save it as data file. Then solve the equations of single DOF system in by using f(t) as input with MATLAB solvers such as ode45.

The white-noise produced by the ‘wgn’ is essentially the band-limited and max frequency is equal to half of the sampling frequency. The ideal white-noise has infinite variance but ‘wgn’ requires to specify it as follows.

Var of wgn = Spectral Ht of white noise required (N^2/rad/s)* sampling frequency(rad/s)/2

In your case choose the sampling time (dt) such that, dt<=1/(2*10*fn), this ensures that the generated white-noise contains the highest harmonic of frequency 10*fn. Where fn=sqrt(k/m)/(2*pi). The factor more than 10 can be used but it is sufficient for lightly damped single dof system.

Then Sampling freq (Hz) = 1/dt.

3. SIMULINK is convenient for this use and it is not required to save the signal f(t). The blocks ‘Band Limited White Noise’ and ‘WGN’ can be used.

Hope this will help.

Note that. the suggestion presented by Chandrashekhar Dharankar.

For JONSWAP, please check:

https://www.researchgate.net/publication/339272195_Development_of_submarine_cable_hydrodynamic_loads_calculation_program_using_MATLAB

For simple PM, please check pages 6 to 8:

Thanks a lot, Dear Armin Huß

I also worked at chimneys on ANSYS.

This is for braced frame,

Thanks

The mode shape is not altered by hysteretic damping distributed homogeneously as a material property, it is simply the amplitude of the response to a dynamic force input which is reduced. This corresponds to a slight out-phasing between the applied force and the response acceleration/displacement, that requires, as rightly said by Alessandro, to use complex (vectorial) formulations.

If the damping model is not hysteretic (i.e. an intrinsic property of the material's young modulus), the physics turn far more complex and the mathematisation non-linear (e.g. viscous or frictional damping). In such cases the mode shape is altered and reveals generally amplitude-dependant...

1. Seismic codes suggest simplified force-deformation models in order to estimate the inelastic behavior both in monotonic and cyclic loading. The monotonic F-δ curve is considered as the envelope and the skeleton curve of F-δ loops under cyclic loading. The real inelastic behavior under cyclic loading depends on the material and the dynamic loading, e.g. reinforced concrete under seismic loading. So, stiffness and strength deterioration should be considered under cyclic loading in the concentrated plasticity modeling technique.

2. Uncertainties about deformation capacity are high beyond the point C of the F-δ curve. Even in the Collapse Prevention performance level (before point C), the ultimate deformations shows significant dispersion in experimental cyclic tests (e.g. reinforced concrete). Consequently, appropriate acceptance criteria for different performance levels and for different materials can be found in seismic codes (ASCE 41-13, FEMA, Eurocode, EN 1998-3, etc) or in other technical literature using model safety factors to scale down the proposed mean values to mean plus standard deviation ones.

Conclusion: Were indeed purely numerical issues. To my surprise beam length errors and node position errors of a magnitude of 10E-6 [m] resulted in a rank deficient Stiffness Matrix.

Hi Milad Cheraghzade

The Python ecosystem is growing and may become the dominant platform for applied machine learning.

The primary rationale for adopting Python for time series forecasting is because it is a general-purpose programming language that you can use both for R&D and in production.

In this post, you will discover the Python ecosystem for time series forecasting.

After reading this post, you will know:

Python is a general-purpose interpreted programming language (unlike R or Matlab).It is easy to learn and use primarily because the language focuses on readability.It is a popular language in general, consistently appearing in the top 10 programming languages in surveys on StackOverflow (for example, the 2015 survey results).Python is a dynamic language and very suited to interactive development and quick prototyping with the power to support the development of large applications.Python is also widely used for machine learning and data science because of the excellent library support. It has quickly become one of the dominant platforms for machine learning and data science practitioners and is in greater demand than even the R platform by employers (see the graph below).

This is a simple and very important consideration.

It means that you can perform your research and development (figuring out what models to use) in the same programming language that you use in operations, greatly simplifying the transition from development to operations.

SciPy is an ecosystem of Python libraries for mathematics, science, and engineering. It is an add-on to Python that you will need for time series forecasting.

Two SciPy libraries provide a foundation for most others; they are NumPy for providing efficient array operations and Matplotlib for plotting data.There are three higher-level SciPy libraries that provide the key features for time series forecasting in Python.

They are pandas, statsmodels, and scikit-learn for data handling, time series modeling, and machine learning respectively.

This article will be helpful

Dear Prof. Armin Hajighasem Kashani, I suppose the following document could give some ideas on how the question posed by you might be addressed. Let's hope for the participation of a vortex specialist in fluid mechanics in this thread.

The mentioned authors emphasize, I unquote then, that "...an identification procedure is used to characterize multiple regions of compact vorticity in the flow fields as series of Gaussian vortices. Significant differences are found between the vortex properties from the time-averaged flow fields and the average vortex properties identified in the instantaneous flow fields....".

Dear Mahdi, although you are using control systems that can not be done directly in SAP2000. However, you can use VBA interfaces to do the same in SAP2000. Same things can be done by matlab.

Thank you Artur Braun for your nice discussion. Could you please suggest an article related to your comments. Also, I want to know why protonic conductivity increase due to annealing through moist N2.

Hi, I recommend the following book

(recent trends in fracture and damage mechanics)

Toan Van Nguyen 1. Because for a continuous elastic solid, there are infinite no. of flexible modes which we generally don't capture while performing the eigenvalue problem. Each of these modes has some mass contributions (much much lower at higher frequencies) which really doesn't make any sense to capture if you're looking for vibration (durability) or noise problems. So in a nutshell, to have the sum equal to exactly 100%, you'll have to capture all the modes of the system which is generally not required for most of the problems out there.

2. This is the paper that I share earlier in my post. It's not my paper :)

Dear Md Iftekharul Alam

Did you find a solution to your problem?

Regards

Ahmed

Hi Mir Aamir Abbas

I believe that it depends a bit.

For unbounded systems, there would not be much of a response before the wave reaches the receiver position. More on this below.

For bounded systems, one must cater for rigid body modes. These have infinite (or a very high) wave speed.

This may at first sound strange, but once we think about it a little, it becomes obvious (or there could simply not be any wave propagation on planet earth which has a high velocity indeed when viewed from the galaxy centrum).

To exemplify, in the case or airbag firing inside cars, there is a pressure increase at the driver's ear before the acoustic wave reaches it. This took the industry about 20 years to figure out and it can be correctly detected when using both pressure transducers and microphones. The former tracks Line Pressure and Sound, while the microphone only tracks sound.

So, for an unbounded system, the 'rigid body' response would still be there, but it would very low and thus something that can be ignored.

Now, let us complicate matters a bit. There is an amplitude dependent portion in wave propagation that causes the wave front to distort - it is referred to as steepening. Simply put, waves with a high amplitude travel faster than the linear free wave speed. After a distance, the peak catches up with the trough and the wave collapses and the process starts anew.

So, when %LP = 100*Pulsation/LinePressure = 100*Sound/Ambient is high, things may happen faster than we would otherwise expect. This is generally the case whenever LP is low, e.g. in vacuum systems, on the suction side of machines and so on.

More on the differences of pressure and steepening is found here. https://qringtech.com/2010/09/15/wave-steepening-increase-peak-pressure-piping-pumps/

I am sure one can compound the issue further if one would want to do so.

Just my 2 cents

Claes

Hi. There are two ways. the first one is to construct a mechanical model to describe the viscoelastic behaviour (in frequency domain) and include it in the stiffness matrix of the model (In this case, the Kglobal matrix will depend of the frequency and you will need use a recursive algorithm to compute the modal parameters). the second way is to express your model in a time domain and use the FFT.

I describe the fist way in my reseach

Uncertainty propagation analysis in laminated structures with viscoelastic core

WP Hernández, DA Castello, TG Ritto - Computers & Structures, 2016

Hi,

First you need to have parameters p that eigen values f depend continously on (aka Young modulus, poisson ratio...). The simplest way to get first order sensitivity matrix s is apply numerical differentiation, such df/dp=s. For this you can use commercial software. Nevertheless, you can also get semi-analytical sensitivity matrix by differentiation of generalized eigen value problem premultiplied by eigenvector. For doing this you need to have an access to finite element stiffness and mass matrices.

Hope it helps a bit.

Hi Eduardo

I have the same issue. I need to do transient analysis of moving load of a real train. Would you be able to help me with this?

Regards

Dear Muhammad,

This could be challenging topics however it is a general one.

1. Analysis of Uncertainty Quantification and Exascale Computing Opportunities and Challenges for Earthquake Engineering.

2. Design, development and characterization study using sustainable materials and rapid monitoring for earthquake engineering

Hope it could work.

Ashish

I think BOARDEX is one of the most comprehensive databases on the composition of boards. It covers various areas of the world (however, unfortunately, it's not free).

I think Anays Rigid Dynamics will give you all the possible options in comparison to any other tool. Try for it to cross verify the results.

Dear professor Kabir Sadeghi ,

Many thanks for the outstanding and magnificent response, which I do appreciate very much.

In the research in community when looking for understanding how the dynamic interplay between structure and shape a simple/complex communities interacted to structures, a community genetics perspective, however, may not be necessary or informative for all studies and systems. To better understand when and how intraspecific genetic variation and microevolution are important in community and structural dynamics, it is suggested that future research should focus on three areas: (1) determining the relative importance of intraspecific genetic variation compared to other structural factors in mediating community and structural dynamic properties; (2) understanding the importance of microevolution in shaping structural dynamics in multi-member communities; and (3) associating genetic mechanisms that drive community and dynamic analysis processes.

hi I am working on the mechanical behavior of Ti-6al-4v on a microstructure level with crystalline plastic theory. But I have trouble to get the hard parameters. for calibrating the hardness parameters with the experimental model, there is not any experimental result on the micro level . How can I get the hardness parameters of this material? best regrads

See the help files.

Hi Mridul Rawat

in my paper is the optimum angle would come between 60-70 degrees

link of my paper is

You can use mixed method sampling (MIDAS) to do the analysis or you convert all the variables to the same frequency. You can search for it on google.

The basic assumption of the random vibration is that you can't predict the actual time realisation of the process, only the statistical measures, which assuming a Gaussian process is the standard deviation. So you can only compare a harmonic and random it in an average sense, which is to have the same input power. And that is what the PSD gives you. PSD is usually approximated as the square of the signal's Fourier Transform. So if you know what PSD value your random process has in a fequency bin, then you can work out what amplitude of sine wave would give similar power. But the only way you can relate the two are through the PSD, comparing actual time histories is irrelevant

The damping model selection is highly dependent on the structure itself. In case of structures having inconsistency in damping distribution, such as the cases of dams, soil-structure interaction models, or controlled structures (i.e. supplemental damping is utilized), in these cases, non-classical damping model is more appropriate for several reasons as follows:

Firstly,

If classical viscous damping model (for example Rayleigh model) is used, it may underestimate the response of the system in some cases and fail to capture the nonlinearity in the system (Val, V.D & Segal, F. (2005).

Secondly,

The main advantage of classical viscous damping model (for example Rayleigh model) is that the orthogonality of the modes is preserved; based on that the classical modal analysis will be, to some extent, similar to the un-damped vibration and easier in analysis. In the case of controlled structures (with dampers), due to the addition of dampers, damping becomes non-classical and the orthogonality of the modes will not be applicable. This means that using the classical damping model (Rayleigh model) will give inaccurate results, Adhikari S. (2000).

Thirdly,

The other main issue with this classical damping model (e.g. Rayleigh model) is the strong dependence on the frequency of the structure as the constants (Alpha and Beta) are evaluated as a function of the frequency. There have been a large number of studies investigating the frequency dependence of the analytical model used in practice, and interestingly the majority of these studies emphasize that material level damping highly dependent on the displacement rather than the angular frequency (Adhikari 2000).

A couple of famous non-classical damping models are “non-viscous damping models” and “frequency independent damping models”. More details can be found in Puthanpurayil etal, (2012).

The issue of simplicity needs comparative analysis study, which I do not have. This may need further investigation. I think it is better to search the more suitable damping model to your system rather than searching for the simplest one.

Val, V.D & Segal, F. (2005). Effect of damping model on pre-yielding earthquake response of structures. Engineering Structures 27, 1968-1980.)

Adhikari S. (2000). Damping models for structural vibration. PhD Dissertation, University of Cambridge

Puthanpurayil etal, (2012), Optimal Passive Damper Positioning Techniques: State-of-the-Art”, book: Design Optimization of Active and Passive Structural Control Systems Chapter: 4

Thank you so much Victor and David. I rechecked my global assembly and found an error in one sign of the reactionary force. That was the culprit!

To Victor, yes, I indeed expected eccentricity to have no effect on the nature of the stiffness matrix. It had to be the assembly error.

Thank you so much to all for taking out time to reply to my question. I highly appreciate it!

Regards

Scale factor is Ig/R, not Ig/2R.

As we input values of I and R while defining load patterns for equivalent lateral load procedure(ELF). Unlike ELF in response spectrum analysis u should input these parameters(I & R) by using scale fctor to get inelastic demands.

Dear Keyvan Aghabalaei Baghaei,

In some situations, the horizontal components of earthquake ground motions can excite the vertical degrees of freedom (cause vibration vertical deformation/vibration). This may happen depending on the structural configuration.

For example, consider a fictitious structure, which looks like the letter “F” with fixed support. In this fictitious example, there are two cantilever beams supported on a column.

If this structure is subjected to only the horizontal component of an earthquake, the column deforms and vibrates as a simple vertical cantilever. This initiates the vertical deformation and vibration of the cantilever beams.

With best regards,

Daniel.

The external forces which are unbalanced in statics (owing to lack of some constraints) are balanced by inertial forces in dynamics.

Good answer.. Nathan Madutujuh ... Following

Hi Ankit Goyal , you may input the rotational ground motion as a rotational acceleration load in SAP2000. To do this, first define a time history function based on the ground motion data you have. Next, define a load case for the acceleration load. Select "Time History" under the load case type. Under "Loads Applied", select "Accel" load type and the rotational degree of freedom under "Load Name". Use your defined function for the rotational acceleration. You may refer to the following websites for more information:

Hi Keyvan Aghabalaei Baghaei, based on the info from Smart Structures: Innovative Systems for Seismic Response Control, if you assume that the K-bracing is rigid without elastic deformation, then the actuator-piston displacement Δ_a(t) = – z(t). I expanded the dynamics for Eq. (5.12) added the electrical system for the actuator.

There are five state variables, namely

z(t) = structural displacement,

f(t) = actuator force,

c(t) = servo valve-piston displacement,

θ(t) = servomotor position,

i(t) = servomotor armature current.

The 6th-order linear model of the building structure with servo valve-controlled hydraulic actuator as Active Tendon System is given by:

M*z''(t) + C*z'(t) + K*z(t) – ag = f(t)

f'(t) = (2*β*A²/V)*Δ_a'(t) + (β*A*K_V*√(2P_s)/V)*c(t)

c(t) = N*θ(t)

J*θ''(t) + b*θ'(t) = K_m*i(t) = T_m(t)

L*i'(t) + R*i(t) + K_m*θ'(t) = V_m(t)

where

T_m = servomotor torque

N = gear ratio (assume that c(t) is proportional to θ(t))

J = moment of inertia of the rotor

b = motor viscous friction constant

K_m = motor torque constant

L = electrical inductance

R = electrical resistance

V_m = voltage source applied to the motor's armature

Please share me the best answer might you get...

This can be very helpful:

Good question.. Please share me the best answer might you trust...

Regards…

Formulate the problem mathematically and seek answers using analytical or numerical techniques, if you have issues with ANSYS. You can also use other programs/software.

This is a calibration for a Viscoelastic Material using a fractional derivative model. There is a experimental data for the storage and loss modulus.

In your problem you must define a inverse problem Ymod = Kelvin_Voigh(parameters), and try reduce (a minimization problem) the error between the experimental response Yexp and the model response.

We have proposed a numerical method (denoted as MEM) for solving the

Nonlinear Dynamic problems. If you would like, you can view our published articles in this field entitled "dynamic analysis of SDOF systems using modified energy method". By the way, the presented idea is also generalized to MDOF systems in another study, which is available on my research-gate account.

if you need more information, please let me know.

Regards,

Jalili

sir,

hiw can I define a hinge and roller support in seismostruct?

Dear Sahra,

I think you need to better formulate your problem. So, at first you have to work out a physical model. Let us start by telling we have water as a medium e,g, solvent in which we have calcium ions dissolved in it. Is this right? Is there any density to the solved calcium ion? This will determine the inter ionic distance rii. There will be a microscopic model of the charge distribution in the electrolyte. The problem can be solved using Coulomb law. It is an electrostatic problem. It could also be solved macroscopically using Poisson equation.

These are some thoughts on your problem that can guide you to find your way?

One advice. The definition of the problem is half of the solution.

Best wishes

Dynamics of Structures by Anil Chopra is the go-to book for most people

Hi, the NOLB method should work, https://team.inria.fr/nano-d/software/nolb-normal-modes/

Dear Bowei,

Thank for your response!

I have solved my problem..

I just change the mass source.. and the graphic shape almost same.

Best regards,

Ichsan

Would you tell me what exactly you want to do? I may be able to help. Thanks.

 Thanks a lot.