Dear all,
I want to initiate dynamic analysis of truss structure to optimize its weight. Kindly get problem definition as attachment.
I considered 10 bar trust of size optimization problem to check & compare results of my program with dynamic constraint.
Considered Area=[35.944 15.530 35.285 15.385 0.648 4.583 23.610 23.599 13.135 12.357];% in cm2 % % Democratic PSO 2014, A. Kaveh & A. Zolghadr
E=6.89e10 N/m2
ρ=2770 kg/m3
Added mass at each node = 454 Kg
Constraints w1≥7 w2≥15 w3≥20
I have coded this problem in MATLAB by using all three theories of dynamic constraint, yet I am not getting exact natural frequencies but getting nearer answer. kindly note all other answers are same except natural frequencies.
For more detail kindly see attachment
Article Democratic PSO for truss layout and size optimization with f...
This can be done through a bifurcation analysis through many engineering and general finite element softwares such as SAP, ABAQUS and ANSYS. Normally eigenvalue analyses were adopted in these algorithm.
Please read the following Book.
NOISE AND VIBRATION ANALYSIS: SIGNAL ANALYSIS AND EXPERIMENTAL PROCEDURES
Anders Brandt
Department of Industrial and Civil Engineering
This can be done through a bifurcation analysis through many engineering and general finite element softwares such as SAP, ABAQUS and ANSYS. Normally eigenvalue analyses were adopted in these algorithm.
Dear @Ghanshyam, thanks for sharing the question. I am not so familiar with a subject, but I have found some papers that might be helpful to You. Regards.
Article On the determination of natural frequencies and mode shapes ...
Article A simple analytic method for computing the natural frequenci...
Article Topology optimization of truss-like continuum structures for...
I suspect that if you ran the problem in a commercial FE code you would get the same results as reported in the original research paper - have you tried this? If this is the case then the results you have generated are up to 4% out in terms of the natural frequencies which is much more than one might expect as a result of using different eigensolvers. As you mention the static results are correct, which implies the stiffness matrix is fine, I suspect there might be a problem in your consistent mass matrix although the matrix definition you present looks correct. Commercial FE programmes, like ANSYS, are able to export element and system matrices so that you could compare these with the ones you have generated. I'd be interested in what you find to solve this problem - also nice to see that you presented the problem clearly.
Easiest way is to go through modal analysis in Ansys where you can get natural frequencies of your modeled structure.
Dear Hi,
The following book will also be helpful, you will find MATLAB code also. Best
Fundamentals of Signal
Processing
for Sound and Vibration Engineers
You can also use a theoretical method, i.e., reverberation-ray matrix method, for this problem.
S.M. Howard, Y.-H. Pao. Analysis and experiments on stress waves in planar trusses
J. Eng. Mech., 124 (1998), pp. 884–891
Y.H. Pao, W.Q. Chen, X.Y. Su. The reverberation-ray matrix and transfer matrix analyses of unidirectional wave motion. Wave Motion, 44 (2007), pp. 419–438
Dear Ji-qing Jiang,
Thanks for your valuable suggestion, I will study this
Dear Angus Ramsay,
Thank you very much.
You are correct There was a problem related to mass matrix.
Hi Ghanshyam, really pleased to hear you have sorted you problem and many thanks for letting us know. Angus.
Dear Dr.Tejani,
I have the same problem as you mentioned and I don't know what's the problem with my mass matrix. Could you share what was the problem maker in your case and how did you solve it?
My modelled truss in OpenSEES is as follows,
model BasicBuilder -ndm 2 -ndf 2 #Two degrees of freedom and two dimensions (a typical truss)
# Nodal coordinations
node 1 0.0000 0.0000
node 2 9.144 0.0000
node 3 18.288 0.0000
node 4 0.0000 9.144
node 5 9.144 9.144
node 6 18.288 9.144
# define the nodal constraints (supports)
fix 1 1 1
fix 4 1 1
# Elasticitiy modulous
uniaxialMaterial Elastic 1 6.98e+10
# The connectivity among the nodes and cross-sectional areas
element Truss 1 4 5 37.712e-4 1
element Truss 2 5 6 9.959e-4 1
element Truss 3 1 2 40.265e-4 1
element Truss 4 2 3 16.788e-4 1
element Truss 5 2 5 11.576e-4 1
element Truss 6 3 6 3.955e-4 1
element Truss 7 2 4 25.308e-4 1
element Truss 8 1 5 21.613e-4 1
element Truss 9 3 5 11.576e-4 1
element Truss 10 2 6 11.186e-4 1
# Added non structural masses on the nodes
mass 2 454 454
mass 3 454 454
mass 5 454 454
mass 6 454 454
# Print the first natural frequency
puts [eigen 1]
And in addition I have asked the same question in a topic entitled as "Finding the natural frequencies of a truss by using OpenSEES?". Available from: https://www.researchgate.net/post/Finding_the_natural_frequencies_of_a_truss_by_using_OpenSEES2#58e22e67f7b67e18ad602942.
Thanks in advance.
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