Vibration Analysis - Science topic

The aim is to study the effect of flow velocity of a certain fluid in a pipe, on the vibrational behaviour of the pipe.

Which is the most crack direction is studied in a metal cantilever beam? When the crack is vertical or horizontal? (I mean if the crack propagates vertically or horizontally?)

And how each type of excitation(Bending, Axial,..) is sensitive for each type of crack shape and orientation?

I am asking for test purposes .. So I can use the crack direction that is more sensitive for measurements in my experiment.

Is there any effect of damage shape on the damage severity? And which do you expect has more severity of damage the holes shape or longitudinal shape? And why?

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..

How to represent natural frequencies and mode shapes in same matrix for many cases for damage detection purposes?

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?

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?

I have calculated the gear meshing frequency of planetary gearbox to be 786 Hz. However, when a FFT is performed on the data acquired for the same planetary gearbox I could see peak around 645 Hz and not at 786 Hz.

The calculated mesh frequency was done based on the speed and number of teeth. But the signals acquired during operation was under loaded condition.

Does external load change the natural frequency and meshing frequency of gear?

Is there any reference to calculate the theoretical gear mesh frequency in relationship with load.

Attached FFT plot.

Thanks in advance for sharing you knowledge.

I am analyzing the squeal of Disc Brake Assembly using Abaqus and I tried to find the unstable frequencies using complex frequency which caused the squealing noise: I am able to find the unstable modes but they are not forming a stable unstable pair. Also, the participation factor is coming for many modes. I am attaching the brake model for reference. Please help me to find unstable frequencies using Abaqus?

I have a simulation code for a Horizontal Washing Machine.

The code solves the equations of motions of the system by Matlab ode45 and plots the vibration response of the system at the transient state of performance.

In this code, the frequency (omega) is an exponential function of time, as it's stated below (and its diagram is attached to 'the question'):

-------------------------------------------------------------------------------------------------------------------------------------------------------

omega= (1-exp((-0.5)*t))*omega_0+(1-exp((-0.5)*heaviside(t-t1).*(t-t1)))*(omega_1-omega_0);

-------------------------------------------------------------------------------------------------------------------------------------------------------

-----------------------------------------------------------------------------

[T,Y]=ode45(@snowa1,tspan1,initial_vector1);

plot(T,Y(:,1)-mean(Y(:,1)))

-----------------------------------------------------------------------------

It is desired to :

First, increase the frequency to omega_0 by exponential1

Then, increase it to omega_1 by exponential2

But 'the problem' is that:

the displacement response shows an unexpected increase in frequency at the beginning of the second exponential increase (it becomes 20 Hz, which is much larger than the maximum frequency in the simulation- 10 Hz).

Do you know what could be the reason for this response?

Any help would be gratefully appreciated.

Can anyone suggest to me method to design fuzzy inference system (FIS) for MIMO structural damage detection (i.e. data distribution on the membership function, parameters of MF, Generate rules ... etc )

In my system there are 3 inputs and 2 outputs:

Inputs: Relative 1st Natural frequency , Relative 2nd Natural frequency , Relative 3rd Natural frequency

Outputs: Crack depth ratio , Crack Length

Note: I tried to use "genfis" By MATLAB it didn't give me reasonable results.

I am doing vibrational analysis of mono-acetic acid after wavefunction and geometry optimisation. In the output file of vibrational analysis the following lines were present containing harmonic frequencies of mono-acetic acid.

****************************************************************

HARMONIC FREQUENCIES [cm**-1]:

-93.9446 -56.8345 -14.9036 79.1124

83.2432 123.7967 180.8622 415.9833

465.7580 564.8411 581.9038 795.9969

942.4123 1030.7040 1139.4888 1218.9753

1356.8784 1433.9457 1447.8727 1776.4078

2976.9823 3023.5483 3084.8354 3634.5117

PURIFICATION OF DYNAMICAL MATRIX

****************************************************************

HARMONIC FREQUENCIES [cm**-1]:

-55.0883 -0.0000 0.0000 0.0000

80.2766 101.0671 159.3476 415.9277

465.5977 564.8100 581.8316 795.9872

942.4062 1030.6968 1139.4801 1218.9731

1356.8769 1433.9456 1447.8725 1776.4022

2976.9823 3023.5483 3084.8354 3634.5117

ChkSum(FREQ) = 0.26286465E+05

Can some one help me understand what is meant by "Purification OF DYNAMICAL MATRIX" and interpret the above results CH₃COOH should have 18 modes of vibrations (3N-6). but I am getting 20 modes of vibrations? Furthermore is -55.0883 cm^-1 a false flag or is it because of incorrect optimisation of structure?

In this picture an experiment analysis by Shaker . What is the conclusion from picture?

Hi All,

I have two vibration signals taken from the same source using two difference sensors. Therefore, the frequency resolution for both the vibration signals is different (One is 1.5 Hz, other is 7 Hz). What methods or tools could be applied to compare both the signals?

Attached are the two signals obtained from the two sensors.

Note - acceleration is Y-axis is considered to comparison.

Hello

I am trying to perform a sine sweep test using OROS 38 DAQ, Modal analysis software and The modal shop shaker 2100E11. The DAQ software allows to specifying the peak to peak voltage from 0 to 10V and I am using natural air cooling for the shaker so the sine peak force is 220 N.

Only accelerometers are available to get the data and no force sensors are available. Is there any way to measure approximate values of force corresponding to the given peak voltage in the DAQ system?

Please help me out with this.

Thank you

i have a project to do the vibration analysis of underwater pipeline hence i dont know from whee to start and how to do please help

while performing i'm encountering error , i'm attaching the mess file and APDL commands

*** WARNING ***                          Entity 3 is undefined.  The MPDELE command is ignored.                 

 *** ERROR ***                            Element type 2 is not the same shape as FLUID30.  Switching to a         different shape is not allowed while elements of type 2 exist.  

please help

I am an undergraduate working on modelling generator noise through an aperture and writing my literature review has been a little extra difficult.

I have been trying to understand the methods of noise analysis in acoustic engineering. There are four of them which are mostly used. And I need to understand each of them to be able to choose the method I would be using in my modelling.

If you have any material, book or journal that could assist me with my research work please do send in, would be very much appreciated.

I would like to ask teachers: many experts have done a lot of research on the vibration analysis of cylinder panel, what is the research background of cylinder panel ? Such as submarines, aircraft, missiles and so on ? Do you have any pictures of this cylindrical panels applied to an actual object ? For example, the cylindrical panels on airplanes and submarines. It is better to have photos of actual objects or paper containing photos of actual objects.

This is the part of the input script. While running the simulation an error is showing

ERROR: Kspace style requires atom attribute q (src/KSPACE/pppm.cpp:208)

# vibration analysis simulation units  metal dimension 3 boundary p p f atom_style atomic neighbor 0.3 bin neigh_modify delay 2 every 1 newton on read_data vibration.data group Platinum type 1 group Argon type 2 group Carbon type 3 # force field pair_style hybrid/overlay lj/cut/coul/long 12.0 eam tersoff kspace_style pppm 1.0e-6 pair_coeff      1 1 eam Pt_u3.eam #Pt-Pt pair_coeff      * * tersoff BNC.tersoff NULL NULL C #C-C 3-3 pair_coeff      2 2 lj/cut/coul/long 0.0104 3.54 #Ar Ar Lj potential pair_coeff      1 1 lj/cut/coul/long 0.5650 1.066 pair_coeff      3 3 lj/cut/coul/long 0.0028 3.14 pair_coeff      1 2 lj/cut/coul/long 0.122 3.311 # Pt-Ar pair_coeff      1 3 lj/cut/coul/long 0.092 3.302 # Pt-C pair_coeff      2 3 lj/cut/coul/long 0.139 3.860 # Ar-C pair_modify       mix arithmetic #---------energy minimization------------------------------ minimize 1.0e-4 1.0e-6 100 1000 min_modify         dmax 0.4 min_style     cg

i have vibration data of bridge and process the data with different possible techniques such as FFT, Wavelet decomposition, Empirical mode decomposition, Hilbert Transform, Frequency domain decomposition, spectrograms, etc. but still i am not able to locate exact or pin point frequency of the bridge structure. in the following techniques the results are in a specific range of frequency such as 2.6 to 3.1 Hz. The data showing this specific range and not providing the exact frequency. because in this range any number can be the natural frequency of the bridge structure. so the actual frequency lies in this specific range but i want to go further in depth to figure out the exact value of the frequency in Hz. but the problem is i am not able to find any technique that will give me answer of my curiosity. i recorded data from accelerometers considering normal traffic conditions. there is not closure of bridge. vehicles are passing normal situation.if anyone have any clue about it or still my question is not clear so i can explain further

i attached some of my results

i will be very grateful to anyone who let me find my answer

thanks

I have been given samples for 'FTIR for vibrational analysis of compounds'.

What short of information i can get through this and how to read the FTIR spetra to right results for nano materials. Is there any specific spectra table for inorganic compounds.

The various parameters taken are:

1. Radius

2. Span

3. Diaphragm arrangement

4. Number of Elements.

5. Boundary condition

6. Cross-section.

Does this include spring-dashpot elements?

I need some help, I have run block lanczos modal analysis in ansys APDL.It shows that the 'solution is done ' . However, there is no any result listed in result summary. How to overcome this problem?

I've run a few simple random vibration analysis such as cylindrical tube and cantilever beam in LS-Dyna. Now, I try to understand the output results in terms of PSD and RMS values.  For instance, if I input a flat acceleration PSD of 0.02 g^2/Hz over a frequency of 0.1Hz to 1000Hz, how can I use this input to hand calculate the RMS von mises stress? I don't mind the math if someone could explain. Thanks

During parameter study for a project (signal processing applied in mechanical vibration), when I decrease the frequency to a very low value (less than 200 mHz, for a interested range of frequency of a few hundred Herz), the frequency response I have gets "squishy" (instead of a single line going up or down, I have a waveform going up or down).

Checking on some forums online yield me the connection to "dirac delta function", but I do not understand it fully. So I'd like to ask if there is any connection between dirac delta function and frequency resolution, with regards to FFT in vibration analysis. Thanks for your help.

After taking the frequency spectrum of an impulse force (from a shaker, sampled from a vibration analysis test), there are noticeable peaks at 50 and 150 Hz (presumably due to some electrical/electronic artefacts or some mismatch impedance between the shaker's coil and its structure). This specific experiment aims to study the effect of frequency resolution on the spectrum.

When the frequency resolution is smaller (same bandwidth, or F_max - F_min, is used, and more spectral/FFT lines are used), these sudden peaks start to appear. It should be noted that the original input signal is the same. The question is why this happens?

Thanks for your help

Hello folks,

i am doing a vibration experiments to analyze the transfer function. But, before that I want to see the effect of FFT-Lines (Band width kept constant) on my experiments. Higher the FFT-Lines will be, finer will be the frequency resolution, which is actually good to analyze the result (if measurement time is not a big factor). Now, I wanna know is there any limitation for frequency resolution? Does my frequency spectrum will not show any change after a certain frequency resolution factor?

Our research is turing to nonlinear vibrations of plates and solids of acosutic wave device strcutures. It is high frequency vibration, and associated phononmena can only be considered with nonlinear analysis.

Please share your experiences and publications on nonlinear Rayleigh-Ritz method with us.

Joint work on the problem is possible for co-authored publications.

I use a piezoelectric actuator for active control of a flexible structure, and measure the vibration amplitude at the same place using an accelerometer. When actuating the structure with a shaker, I see less noise, but when actuating with the piezoelectric actuator, there is too much periodic noise in the response, and it is not usable.

Any idea how I can reduce or remove it?

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 am conducting a project where underground blasting effects are analysed on soil and structures above the soil. I've currently only have a very basic Abaqus model of a soil block with an implicit dynamic step. A time history amplitude was induced on this basic block model of soil. It shows the stress wave propagations. It has parameters for the Mohr-Coloumb plasticity. I am looking for books or any literature to further understand how the vibration of the blast will effect the soil layer, and possibly different layers of soil (rocks, clay, silty, soil etc). Any help or advice is appreciated!

Dear friends

I'm working on the validation of an FIV case, which for making phase difference between force and displacement, I used an initial velocity in the structural, but after several coupling step, the drag force becomes constant, therefore the structure doesn't fluctuate, the drag force is more than the amount mentioned in the original case which shows vibration in the structure.

any suggestion will be appreciated

In ABAQUS help I read the applications of direct solution in steady state dynamic analysis as follows , what are the examples of applications and where I can NOT use this method ? I would appreciate a comprehensive answer , thank youhttp://ivt-abaqusdoc.ivt.ntnu.no:2080/v6.11/books/usb/default.htm?startat=pt03ch06s03at09.htmlThe direct-solution steady-state analysis procedure can be used in the following cases for which the eigenvalues cannot be extracted (and, thus, the mode-based steady-state dynamics procedures are not applicable):

Damping of oscillation by interstitial atom movement through lattice shows a damping peak. Why the damping is frequency dependent, while interstitials transit from site to site, and restoring forces are not strictly hookean? An article claims, such fitting of damping data with mechanical impedance models have no theoretical justification, ( , , )why?

Hello,

I want to analyze a wheel-tire system. In order to do that I need Young's Modulus, Shear Modulus, Loss Factor and Poisson's Ratio. I have already checked some articles but I need a specific TPE or rubber. Because I will produce this system after my analyses. How can I find these properties?

Thank you.

I am trying to regenerate the Natural Frequencies of a clamped-clamped viscoelastic core via. ACM (Approached Complex Eigenmodes) method as is in the article : "Linear and nonlinear vibrations analysis of viscoelastic sandwich beams" (DOI: 10.1016/j.jsv.2010.06.012).I am trying to use semi analytical Galerkin method in order to do so. the problem with the use of ACM method for modeling the core my answers are close but when I increase the number of modes to solve the problem in more precise way my answer get worse! and also there is no convergence happening with increasing the number of the modes. what the problem could be? and would it be a better approach to solve the frequency dependent problems which wouldn't be highly costed in solving?

I have been doing research on extracting information like acceleration, distance, etc. from an analogue signal by performing analogue signal processing on any type of signal. I haven't found any certain techniques which would help me in providing a formula or any sort of information which would lead to extracting information by analogue signal processing. If anyone is aware of analogue signal processing, could you please enlighten me if it is even possible to do this?

After spending hours, I am at a stage where I feel like it's not even possible to do this.

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

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)?

Thank you in advance for your input and time.

I am looking for ways to do vibrational analysis for the molecule I studied. But I found very little about how to self-define coordinates. And I don't know the meaning of 's' or 'k' in the first column of automatically generated .dd2 file.

Does anyone know the logical way to do it?

I am using FFT(Matlab) to convert time domain curve in frequency domain but it is showing me the number of samples in X-axis instead of frequency. How to obtain the frequency in X axis in frequency domain curve obtained from time domain using FFT?

I have frequency domain result for pressure. After converting it to time domain by applying inverse Fourier transform it's amplitude is changing. It is not matching with the respective (1/frequency) values in time domain curve. Is there any normalization applied while converting by inverse Fourier transform?

Hi all

in an HCF analysis for a Shell body, how do I use probability in Stress level in wohler curve ?

We know that IRF for an SDoF is:

h(t-ta) = ( 1/m*w_d ) * e^{- kesi * wn * (t-ta)} * sin( w_d * (t-ta))

what is the form of an MDoF function, with this in mind that we do not want to use modal analysis to decouple the equations?

I want to do a free vibration analysis for a plate. In this research, I want to use the Ritz method. For Ritz-shape functions, which are the best polynomial functions that give the most accurate answer?

Hello everyone!!!

I am very curious to know about the real life applications of various elastic foundations such as Winkler elastic foundation, Pasternak elastic foundation etc.

Thank you in advance

Hello everyone,

I want to simulate SKF bearing 6308 in ANSYS Workbench explicit dynamic. I created the model as below, but for simplifying the model, I used 3 balls for the bearing. 

The inner race of the bearing has a local fault. As it clear on the outline, I used frictional contact (coef=0.005), an angular velocity of 1000 RPM for the inner ring, fixed support of the outer surface of the outer ring, and end time 0.018 (for one complete revolution). I did not consider any radial load. After solving the problem, I realized that only the inner ring rotates and the cage and balls slip a little (3-5 mm). For this problem, I changed the frictional coef from 0.005 to 0.1 and even no separation. But, still, I did not see any rotation in balls. They just slip a bit with the inner ring. One more time, I assigned clearance between balls, races, and the cage. Again, it did not work (clearance 0.01 mm).

It was weird why balls do not follow the rotation of the inner ring. As a result, I created a simple model similar to bearing the cross section with a ball between them. As shown in the picture below. 

By moving the upper part to the right, again the ball remains constant without any rotation. It just has a bit displacement (slipping). 

I really appreciate if anyone can help me step by step to solve this problem. 

Thank you. 

I'm trying to solve motion equations of one degree of system with tuned mass damper. the principal mass is subject to withe noise excitation. how can i have obtained the frequency response and the temporal response??

Hello,

A structure is tested for a Random Vibration (say Z axis, 0.1PSD, 20-3000Hz), where I obtained response acceleration from measurement system. Now I wanted to obtain same output(amplitude of modes) by giving Harmonic(sine) sweep as input(in Frequency domain) to Shaker machine. I read some on-line papers explaining conversion/equivalence from PSD to harmonic but none of them are actually working. Can someone please refer some good source?

Thank you,

Hi All

For an ndof vibration system of mass and dampers, we know the equation of motion for imposed force.

but in finite element codes, it is also possible to apply a constant displacement and calculate the reaction force in the fixed end of the system as the response function .

Anyone could help with how to write the equation of motion for such a vibrating system ?

What are the advantages and disadvantages of performing numerical integration from acceleration to displacement in the time domain and frequency domain, respectively?

I use Ansys to perform random vibration analysis. But I have a doubt about the input load spectrum. Is the amplitude of the input load spectrum force fitted in the normal distribution model such that the maximum load recorded ( from road load data acquired) equal to the 3-sigma load?

doing a project related to a plate and its vibrational analysis in the presence of fluid surround itself.

I've found several iPhone accelerometer and Android accelerometer apps (for example http://www.iseismometer.com and http://www.now-instruments.com/products/3-vibsensor ).  Are these useful for doing quantitative vibration analysis in the lab, and if not, what are their deficiencies?

I am currently studying the behaviour of a cantilever beam and I need to obtain the damping factor of each mode of the beam. Does anybody know how to do this?

I have the time-response of my beam that I have obtained with an accelerometer but in this time response all modes are together.

I need the different damping factors in order to be able to obtain the rayleigh coefficients of my beam and simulate it in Abaqus.

I have read that I can obtain these dampings factor with the bode diagram, but I dont know how to obtain bode's diagram out of my time-response graph.

Or even how to isolate one mode and that the accelerometer only registers that mode.

Thank you very much!!

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 ?

Hi all!!!

I am trying to obtain frequency parameters of one dimensional nano-structure which is placed on an elastic foundation by using MATLAB code. But I am getting complex numbers (purely imaginary) and complex conjugates for frequency parameters . What do those imaginary values mean and why am I getting this?

Thank you in advance.

I want to start working on the generalized differential quadrature (GDQ) method to solve the problem of the mechanical behavior of beams, plates and shells.

Dear colleagues, I hope to give some suggestions (papers, books, etc.) and simple examples for work on this method.

I want to start working on the generalized differential quadrature (GDQ) method to solve the problem of the mechanical behavior of the beams, the plates and the shells.

Dear colleagues , I hope to give some suggestions (papers, books, etc.) and simple examples for work on this method.

I am trying to find the nonlinear frequency of plate. I have just started working on "Nonlinear analysis of plates and shells". Can anyone suggest the better iterative scheme for finding the nonlinear frequency of plate?

As is well-known, there may exist some paradoxes when one uses the nonlocal differential type constitutive equations. For example, the fundamental frequencies of the structures increase with increasing nonlocal parameters, and when the nonlocal parameters exceed to some values, the higher mode frequencies vanish [1-3]. Obviously, this paradox does not agree with the fact that the inclusion of nonlocal parameter makes the structures softening. Therefore, it is of great necessity to develop a method to overcome this paradox. Luckily, the variational-consistent boundary value problems (BVPs) have been developed recently [4, 5]. The numerical results clearly show that the modified BVPs can result in the expected softening effects for structures with clamped-free boundary conditions. Additionally, the BVPs for other constrains can also yield the same results compared with Lu et al. [6] and Wang et al. [2]. Therefore, the present method is effective for solving the paradox for the dynamic cases. However, this method is not applicable for the static case. Hence, I recommend the authors use the corresponding integral type constitutive equations, although it is reported that the common integral type nonlocal constitutive equations may induce the inconsistence [7, 8].

Analogously, the present method can also found to be effective for solving the inconsistences encountered [9]. I think, form this point, that building the relationships between the nonlocal strain gradient theory and its corresponding integral type are going to be an interesting topic.

References

[1] P. Lu, H.P. Lee, C. Lu, P.Q. Zhang, Application of nonlocal beam models for carbon nanotubes, Int. J. Solids Struct., 44 (2007) 5289-5300.

[2] C.M. Wang, Y.Y. Zhang, X.Q. He, Vibration of nonlocal Timoshenko beams Nanotechnology, 18 (2007) 105401.

[3] X.-F. Li, B.-L. Wang, Vibrational modes of Timoshenko beams at small scales, Appl. Phys. Lett., 94 (2009) 101903.

[4] X.-J. Xu, Z.-C. Deng, K. Zhang, W. Xu, Observations of the softening phenomena in the nonlocal cantilever beams, Compos. Struct., 145 (2016) 43-57.

[5] X.-J. Xu, M.-L. Zheng, X.-C. Wang, On vibrations of nonlocal rods: Boundary conditions, exact solutions and their asymptotics, Int. J. Eng. Sci., 119 (2017) 217-231.

[6] P. Lu, H.P. Lee, C. Lu, P.Q. Zhang, Dynamic properties of flexural beams using a nonlocal elasticity model, J. Appl. Phys., 99 (2006) 073510.

[7] G. Romano, R. Barretta, M. Diaco, F.M.d. Sciarra, Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams, Int. J. Mech. Sci., 121 (2017) 151-156.

[8] X. Zhu, L. Li, Closed form solution for a nonlocal strain gradient rod in tension, Int. J. Eng. Sci., 119 (2017) 16-28.

[9] X.-J. Xu, B. Zhou, M.-L. Zheng, Comment on “Free vibration analysis of nonlocal strain gradient beams made of functionally graded material” [Int. J. Eng. Sci. 102 (2016) 77‒92], Int. J. Eng. Sci., 119 (2017) 189-191.

Currently I'm doing a project to analyse vibration data of Induction Motors to identify different kinds of faults that they can have. For that I would like to get more samples with various inductions motors having different faults (ex: Mechanically Loosed, Bent Shafts, Bearing Faults, Unbalanced etc.) in order to have a more accurate analysis. If someone have such data, I would like to collect them.

In the article titled "NURBS-based isogeometric vibration analysis of generally laminated deep curved beams with variable curvature" have been presented non-dimensional natural frequencies for layups [45/45/45/45] and [30/30/60/60]. Therefore the problem's formulation still stands for these layups. I have 2 questions:

1. Why the D16 and D26 stiffness coefficients for these layups have been considered to be zero, and in other words, there is no coupling between bending and torsion?

2. For which other layups it is not anticipated to there will be a coupling between bending and torsion?