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# Structural Dynamics - Science topic

Explore the latest questions and answers in Structural Dynamics, and find Structural Dynamics experts.

Questions related to Structural Dynamics

I'm currently do my final year project, I use time integration method to solve linear dynamics structure.

Dear Researchers Greetings,

I'm trying to model a structure under earthquake loadings, I want to investigate the structure's non-linear behavior.

I went through a lot of papers in the literature. Besides those who rely on finite element method and modeling software (i.e., SAP2000, ETABS, Openssen ...). A few papers use the lumped mass system to represent structural models and introduce a hysteretic restoring force that reflects the inelastic behavior of the structure. This force is calculated based on the hysteretic behavior model presented by Bouc and Wen.

My question is, How accurate are the models based on this approach? If there exists an alternative to this approach please let me know.

Warmest regards.

I have developed a particle reinforced metal matrix composite for a specific application that require a static,dynamic and couple field analysis. May I know the procedure to perform these modelling and analysis of MMC products using Ansys or any other specific software.

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).**

- Can this be considered to be strictly true?
- 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?

Jerk is defined as the rate of change in acceleration. But I would like to know some practical applications of Jerk inorder to have better understanding. I kindly request to suggest me some examples.

Of course, set the damping ratio of a structure to 5% will simplify the dynamic calculation. However, we all know it is just an assumption and since structures are quite sensitive to their "real" damping ratio, especially when the frequency ratio is near the unit. I wonder how we can achieve an actual damping coefficient numerically?

Hello Researchers,

I am using Gauss Quadrature for numerical integration to obtain the stiffness and mass matrices for a plate element in my FEM code. We know that both these matrices are symmetric. However, I find that due to numerical integration the stiffness and mass matrix turns out to be

**.***asymmetric*Kindly note that the

*is not by any means large. The result of the subtraction of a symmetric matrix from its transpose is a null or zero matrix. If I subtract the stiffness and mass matrix from their respective transposes, the resulting matrix has all the non-diagonal terms of the order 10 to the power of -8 and all diagonal terms are zero (maybe for most cases it can be considered as a zero matrix).***asymmetry**At the point of writing this question, I am suspecting that this discrepancy (i.e asymmetry of the mass and stiffness matrices) is due to the finite precision arithmetic of floating-point numbers. (need your thoughts on whether my suspicions are true)

The end result of not having symmetric stiffness and mass matrices is that the 'eig' function in MATLAB gives incorrect eigenvectors although the eigenvalues are correct.

I would like to know if anyone has encountered such issues and how was it resolved.

I am also attaching a couple of links related to finite precision arithmetic errors below for your reference:

Thank you,

Jatin Poojary

I am going to model a three-layered circular plate with a magnetorheological core in Abaqus CAE 2016 . is there a way to model the MR material without writing subroutines, simply in the property module for example?

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 mean the use of the SQUG database to assess the seismic resistance of NPP equipment with the specified type of reactor.

Hi everyone,

to calculate the prying forces in the column base plate connections, we need to get the contact reaction between the plate and the concrete, but in my model, I have a part in compression and another one in tension. so how can I evaluate the surface of the plate in tension under the cyclic load ?

So I am beginner in Random vibration research. I have gone through some theory like ergodicity, stationarity, PSD etc.. related to Random Vibration. I am trying to model a very basic SDOF system subjected to random vibration.

I am trying Python. I have already modelled a harmonically loaded linear vibration system. For that I just needed to solve the equation of motion. But I am confused regarding incorporating randomness. How and where I use

How can I move about ? What are the baby steps that I should take ?

I am interested to perform spectral analysis of a structure under random waves. could anyone suggest me a book or an example that starts from wave spectrum (such as

**, P-M etc) to RAO. A complete example from formulation to numerical evaluation.**

*JONSWAP spectrum*The summary can be accessed from the link below:

Please let me know whether the information that has been gathered in the summary file is informative or not.

If the summary description is not clear enough, any suggestions will be welcome.

Any suggestions? Provision of restrained braces in the frame.

hello everyone can anyone please suggest me book on structural dynamics?

"I have mode shapes and eigen frequencies from FE simulation. I have modal matrix and eigen frequencies corresponding to each mode. The mode shape is mass normalized. I am required to correct each mode for damping, i.e to add 1% modal damping to each mode. do you know how to add 1% damping to each mode. what should I do

Structural dynamics, Vibration, modal analysis

Dear researchers

As you know, one of the challenges of using nonlinear procedures is to determine the behavior of plastic hinges of members with deformation controlled action that this behavior is assigned to the plastic hinge by a force-deformation curve and its relations using parameters modeling. various researches has shown that the uncertainties in these modeling parameters significantly affect the structural responses.

Also, the acceptance criteria of different performance levels relating to the mentioned force-deformation curve are needed for performance-based design of structures.

There are two questions now:

1- Are force-deformation curves presented in ASCE 41-13 suitable only for nonlinear static analysis (push over)? or also is applicable for nonlinear dynamic analysis?

2- Given that the acceptance criteria presented in ASCE 41-13 are derived based on the mentioned force-deformation relations in this code (a, b and c modeling parameters), what acceptance criteria can be used to evaluate the structure at the IO, LS and CP performance levels if the other force-deformation relations presented in the technical literature (such as Lignos and Hartloper relations for beams and columns of moment frames, respectively) are utilized for concentrated plasticity modeling?

The mentioned curves (Lignos and Hartloper relations) are mostly used in structural modeling to study the structural collapse, in which the collapse is determined by the criteria mentioned in FEMA p-695 and as a result, acceptance criteria in accordance with these behavior curves have not been researched.

Hi,

I am trying to model a free-free body (aircraft) as a stick-model only consisting of beam elements. For certain configurations I observed that my Stiffness Matrix loses singularities / my model has an insufficient number of rigid body modes. I broke the problem down to a simple 2-D Beam configuration shown in the attached picture. The model consists of 5 Nodes with 3 degrees of freedom per Node all connected via Euler-Bernoulli-Beams with the analytical Stiffness Matrix shown in the picture. The left configuration exhibits the expected behaviour having 3 rigid body modes. Introducing the additional stiffening beam element for some reason reduces the number of rigid body modes, as indicated by the higher Mode 3 Frequency and the higher Rank of the Stiffness Matrix. Is such behaviour expected? And if yes, what are ways to workaround this problem other than building the model from 3D solid elements?

Thanks for your help!

by time series, i mean the structural dynamic responses

I am modelling a piezoelectric material bonded on the host structure & correspondingly I have to plot electrical conductance vs frequency plot.

I have been doing the work in Ansys apdl & following this video by Sailesh sir. https://www.youtube.com/watch?v=JEvVicDzYl0&t=116s

In a harmonic analysis of PZT, I need to add rayleigh damping coefficients values (alpha & beta) in software, but I don't know what are rayleigh damping coefficients for concrete.

Any help would be appreciated. Thank you

As shown in the figure attached, the turbulent fluid flow around a floating (i.e. partially submerged) cylinder with a rectangular cross-section is to be modelled. Clearly, the forces and torques acting on the cylinder are oscillatory due to the vortex shedding phenomenon. The ultimate goal is to study the cylinder stability on the surface. The question is then how to characterize the fluid forces. Particularly, I have no idea if such a stability analysis could be based on the time-averaged forces or the instantaneous values may play a dominant role. How to characterize and quantify the significance of time-averaged values versus instantaneous values in this specific application?

I would appreciate any comment.

Greeting dear researchers,

I'm interested in non-linear behavior of structures (mainly buildings) and I'm looking for a model to simulate this behavior using a lumped mass system and solved in state space representation, I came into few papers dealing with such problem (papers are mentioned bellow) however the exact method used is not clear or detailed.

Thanks for reading and answering in advance.

1. Cimellaro, Gian Paolo, Oren Lavan, and Andrei M. Reinhorn. "Design of passive systems for control of inelastic structures."

*Earthquake Engineering & Structural Dynamics*38.6 (2009): 783-804.2. Reinhorn , A. M., Oren Lavan, and G. P. Cimellaro. "Design of controlled elastic and inelastic structures."

*Earthquake Engineering and Engineering Vibration*8.4 (2009): 469-479.Protonic defects has been used several times in discussions of protons existance in high temperature proton conducting metal oxides. When I read some articles, I got difficulty to understand what really the proton defects stand for either is for the excess or absence of protons. which one is proper? More challengingly, is when hydrogen defects used instead of proton defects. i.e. Sentence substracted from one article: The structural, dynamical, and electronic properties of ionic defects in ........created by the addition or removal of a proton have been studied using the method of ab initio molecular dynamics. These protonic defects correspond..............

Fracture mechanics

Structural dynamics

Earthquake Engineering

Structural Health monitoring

Hello,

I am working on the structural dynamics of a rocket. In a free-free condition of a rocket, the modal effective mass of the fundamental mode is zero since 100% of the mass is participating in rigid body modes. But in a paper (attached below page:53-54), modal effective mass is computed for the fundamental mode considering a rocket in free-free condition. So want to know how to compute the modal effective mass

for the fundamental mode in free-free condition, any related reference would be helpful to understand.

Thank you

I am trying to validate my drop mass impact test results with ABAQUS/Explicit impact simulation. The specimens were bare and CFRP wrapped CHS steel tubes. I got good agreement in case of bare column. However, in CFRP wrapped columns I'm facing problems in capturing contact force-time response of impact tests. The displacement time curve of CFRP wrapped tube reasonably agreed with tests considering the complexity of the model. Please find here mid span displacement and contact force time history comparisons as attached picture with this thread. I have used continuum shell elements to model CFRP and cohesive elements to model adhesive between the layers.

I'm wondering whether continuum shell is capable of capturing the contact force response such dynamic problems or I have to used 3D solid elements by using VUMAT subroutine. I will appreciate if anyone can provide me with any help on this issue.

Many Thanks.

In a structural dynamic wave propagation problem, is the displacement at a point a continuous function of time or is it a continuous function of time only after the wave reaches the point?

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 am solving finite element model updating problem. In order to achieve that i am studying inverse Eigen sensitivity method as a updating method. There, i am unable to understand how to calculate sensitivity matrix. Can anyone help me with small numerical example to calculate sensitivity matrix.

Hi everyone , I need to model a moving load in ANSYS. I want to model the movement of a train on a bridge. IS there anyones who can help me with this issue??

I did my masters in Structural engineering and want to pursue a PhD in EQ. plz, guide about demanding research topic in EQ and Structural dynamics.

Dear Researchers,

I'm looking for a database on corporate governance structures (board composition, CEO duality, independent and non executive directors, etc.) and their change through time for US-based listed companies.

Do you have any suggestion?

I would like to thank you all in advance for your contributes.

hallo, i am doing rescale use acceleration of spectral response target and spectral response from TH(ie kobe) for 0.2T until 1.5T, where T from natural period building.

do it correct for 1 pair earthquake ( UX,UY), then i scale to response target?

or from 7 ground motion i make average, then scale to response target?

because my spectral cant like my target.(attach)

or i must do scale from base shear from result my response spectrum and my time history?

thank you

Hey,

I am working on the Multi body dynamics of a 300kW VAWT as part of my graduation thesis. I have created a reduced order model of the turbine using SIMPACK (MBD solver from dassault systems). I am facing some difficulties with running modal analysis due to error in modal matrix being singular.

I am reaching out to people who have worked with SIMPACK, hoping to get some help with my model .

Regarding design of a dam(or any similar solid monolithic structure), from Structural-Dynamics point of view, with/without computer coding(e.g. Matlab, Python, etc.); how can we compute Modal-Mass and Modal-Participation-Factors?

In addition to that, by which method can we compute the dam response when subjected to any specified horizontal ground acceleration(such as horizontal contribution of the seismic excitation)?

How to choose a community that would be a candidate for restoration in certain region, and create a community model that addresses the questions regarding composition, interactions, structure, and dynamics ?

Hello, everybody! Recent, I have a problem about the fitting of the material parameters. I use the hardening model that proposed by

**Asaro**in**crystal plasticity model**, but I don't know how to fit the material parameters(C11, C12,C44, h_{0}, g_{inf}, g_{0}, C, D).Who can tell me the method about the fitting of the material parameters ?

Thank you in advance!

Is there any relationship available to relate brace angles and lateral displacement in steel diagrid building ?

I am looking for possible optimum brace angle which result in low lateral displacement.

How do I use mixed frequency ( i.e. a combination of monthly, quarterly and annual data) in a structural dynamic factor model for macroeconomic shocks analysis e.g. Stock and Watson (2012) -

*Disentangling the Channels 2007 - 2009 Recession*(not for nowcasting or forecasting)?Thank you.

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,

I have a multi-storied structure with 3 DOFs at each floor. first 2 translations in X and Y and third being rotation in Z. I am trying to assemble a global stiffness matrix from local stiffness matrices.

I have included local eccentricities in X and Y to account for plan irregularities in the modelling.

This is how my local stiffness matrix looks like.

Ke(:,:,f) = [K1(f) + K1(f+1), 0, -ey(f)*(K1(f) + K1(f+1));

0, K2(f) + K2(f+1), ex(f)*(K2(f) + K2(f+1));

-ey(f)*(K1(f) + K1(f+1)), ex(f)*(K2(f) + K2(f+1)), (ex(f)^2*(K2(f) + K2(f+1)) + ey(f)^2*(K1(f) + K1(f+1))) + K3(f) + K3(f+1)];

Here f and f+1 denote the quantities at floor level f and floor level f+1, ex and ey are the eccentricities in X and Y, K1 is the net lateral force in X and K2 is net lateral force in Y.

I am having trouble in assembling a global stiffness matrix from the local one.Weird part is that, the same code runs perfectly well for regular building with small eccentricities. As soon as I change the plan to an L shape or a C shape where Centre of Mass and Centre of Stiffness drift apart quite a bit, the stiffness matrix changes so much that the natural frequencies are imaginary and the solutions blows up.

Can anyone please guide me?

I am Doing project on scale factor. i.e. base shear scale factor. in the manually calculation we dident use any type of 1st scale factor but in etanb 16 we use 1st scale factor as the Ig/2R. also i want to know that why matching is done in static and dynamic analysis.

Why are horizontal degrees of freedom (DOF) mainly considered in the dynamic equation of motion rather than other DOFs such as vertical and rotational for control of structures?

I understand that when solving a static problem, the stiffness matrix is normally singular and that adding specific restraints is what yields a unique solution to the problem. But in dynamic problems, this issue doesn't arise even if the same concept applies, which is the system will have a rigid motion. So, why I don't get the same error when solving dynamic problem. I tried that using SAP2000 by analyzing a frame system without specifying any supports. the static analysis gave errors while the dynamic analysis didn't. So, why?

I have used the Galerkin method in order to acquire the Mass and Stiffness matrices and by calculation of the natural frequencies and comparing them with FEM software, the matrices seem to be valid. I have to say that the assumed mode shapes of the problem are of the Bessel kind. by the use of foresaid matrices and 'ode45' solver of MATLAB when it comes to time dynamic response to the mentioned load, the solution always diverges. the force matrix is already validated by checking the static response of the plate. I have reduced the time step, time span, relative and absolute tolerances and also set the 'NormControl' option to 'on' in order to reduce to solution's errors but unfortunately nothing changed. so what the problem could be? should I change the solver to another one such as Newmark-Beta ? by the way, the Mass matrix determinant is about 0.006 and is a little close to singularity but it haven't caused any trouble in calculating the natural frequencies where we need the inverse of this matrix the same as calculating the dynamic response, however in calculation of time response I have used 'pinv' function for the inversion of the Mass matrix, which is used in such cases to increase the accuracy.

I used a frame structure to represent a continuous shell plate and this frame structure was calibrated with a physical model in order to have the same rigidity as the real one. However I was trying to identify how representative would if a change the thick of the frame elements to represent a shell plate.

Thank you in advance.

I am working on rotational seismology, and I want to give rotational ground motion data as a input in SAP 2000, and want to check the torsional mode shapes of structure, and want to study about effects of rotational component of ground motion data, If any other software is available for this purpose then please suggest me that also.

I have modeled a multi-story building structure equipped with active tendons systems. I am using sliding mode control method to decrease the dynamical responses of building in MATLAB.

Using the sliding mode control law in the state space form of the systems as dZ/dt=A*Z+B

_{u}*U+B_{r}*ag, I can calculate the sliding mode control "force" as U=-inv(P*B_{u})*(P*A*Z+B_{r}*ag)-eta*sign(P*Z).I wonder if I need to consider the actuator properties of active tendon system in order to obtain the voltage/current signal. If so, considering my work as a numerical study, I would appreciate any comments or references on this issue.

Regards,

Keyvan

We're using the Cross Multiscale Sample Entropy to real data recorded during a low intensity seismic event for damage detection purpose.

We're obtaining good results with Spectral Entropy (SE) and we want to compare them with the ones obtained with the Cross Multiscale Sample Entropy (CMSE).

The problem is related to the length of the time series: we can use the SE on the whole recorded signal (16,000 samples), while we cannot employ the CMSE. In fact the CMSE works only on a very short portion of the signal (3,000 samples).

Consequently with the CMSE we’re encountering computational issues due to the long time series, as well as problems related to the presence of seismic input.

We know that the CMSE is independent of the time series length when the number of data points is larger than 700-1000 samples. But this is true for stationary problems.

We didn’t find anything applied in civil engineering problems with this conditions.

Does anyone know how to overcome this problem?

Thanks!

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 want to find ductility of structure by using pushover analysis in ETABS 2015. Can anybody tell me the procedure for doing same.

I had solution for sandwich beam with viscoelastic core. The properties of viscoelastic material is taken in the form as

E = E ' + i * E " or E = E ' ( 1 + i * eta ) ; where eta (loss factor) = E " /E, where E ' = Storage Modulus, E " = Loss Modulus.

I would like to verify the solution using ANSYS. But I couldn't find the way to define the E' / E" / eta in ANSYS APDL.

Dear researchers,

the evaluation of the structural damping can be accomplished using either classical method such as Rayleigh damping or Modal damping these methods assume a proportional damping related to the mass and rigidity, or non-classical methods that are more complex and costly.

In this question I want to know which method is recommended and among the non-classical methods which one is the most complicated and which one is the simplest.

Warm regards.

I want to explore the dynamics of parametrically excited (nonlinear) beam whose material's Young's modulus (E) and loss tangent (tan(delta)) are known. It is convenient to use the simple Kelvin-Viogt model in the evaluation nonlinear dynamics. Hence, I want to find out viscoelastic coefficient (eta) in the model,

sigma = E*(epsilon)+eta*(d/dt(epsilon))

where, sigma is time varying stress, epsilon is time varying strain. d/dt is differentiation with respect to time.

Please, give me some suggestions for the calculation of viscoelastic coefficient or any other alternative modelings using loss tangent and Young's modulus.

On what parameters the selection of continuation method depends ?

SeismoStruct and Opensees programs.

task description: an inverse numerical-experimental approach is used to determine orthotropic material properties.

Experimental determined eigenfrequencies are used to fit the FEM model with the help of an optimization method the discrepancies were minimized to a minimum and homogenized material properties are determined.

Question: So as this is an undertermined problem how the determined orthtropic material porperties could be improved to be physically true and not only mathematically fitted?

thanks

Hi everyone.

This might seem a bit vague but i need some direction. i have run classical molecular dynamics simulations using different potential parameters from literature and want to compare which is the best at simulating the properties of calcium ions in water. I have radial distribution functions, angular distribution functions and vacf data as well as the mean residence times in the first and second hydration shells. I need a way to compare this data with my reference data obtained using ab initio md.

please let me know if you can point me in the right direction.

Thank you.

I am working on macromolecular complex structure and dynamics analysis. The complex has RNA molecule. What is the appropriate way to perform NMA on RNA-protein complex? Also, is there any size(nt) limit of RNA structure to do the NMA analysis.

I am currently modeling a simple truss with Newmark Method (time integration method) on SAP 2000, I have read some of article about process of time integration method.

But since I try to compare the "show plot function", it has different shape with the time history input. (please take a look to the picture below)

Anyone who ever use linear time integration method specially newmark method. I hope you have time to help me.

Regards,

Ichsan

Hi, everyone.

there are many papers about river plume. But each paper looks from a different facet such as salinity, temperature distribution, density, currents and etc. I need a book to know river plume system basically and comprehensively. can any one offer the book?

thanks a lot.

I'm going to do research in this field, so any contribution is appreciated.

I found that Newmark method is widely used in the research of structural dynamics and nonlinear dynamics. What is the advantage of this method over Runge-kutta method when solving structural or nonlinear dynamic equations?

Hello,

can any one explain to me how the gain matrix K in the picture attached is obtained? normally we have u(t)=-1/2 R

^{-1}B^{T}P x(t) instead of this one in equation (4) .The whole paper is also attached.

Thank you

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.

I am designing a 110 storey building for different innovative structural systems, I have carried out the elastic design and the design is governed by wind loads for drift considerations. Now I want to carry out the performance based design of these systems , I did try pushover analysis in MIDAS Gen software for response spectrum as per IS-1893(2002) , but my capacity is much greater as compared to the seismic demand.Thus all the systems are still in the elastic region. Now I want to carry out a pushover for Wind loading, is it possible ? Can I carry out time history analysis for Wind loading ? Please help.

i have modeled the RC beam with simply supported BC and used concrete damaged plasticity model to account for the nonlinearities in concrete, i have got the frequency value for the case of beam under its own weight only, i want to add loads to it to get values of frequencies for cases.

i have used a static general step to define the added load, knowing that this step is before the frequency step, but the results of frequency are not even close to literature!

i'm attaching two models one without load which has a first frequency of 43.79 cycle/sec which is equal to 267 rad/sec , that is close to the value in literature, my problem is when i add the load in the other model, i added here for example 800lb =3558.577 on each hanger of the beam , cause the loading is applied on two hangers as shown below, the frequency is not even close, it's almost the same as the case without loading.

i have attached the paper "by Jerath and shibai" i'm getting information from to model

i have also attached the beam scheme noting i have used the reinforcment as in series 1

i have used a CDP model based on a python code attached here that is based on a paper by carriera and chu also attached !

can anyone help, please?