Eigenvalue analysis of a simple beam

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devilmaycry
Posts: 6
Joined: Tue Feb 05, 2013 3:37 am
Location: Iran

Eigenvalue analysis of a simple beam

Post by devilmaycry » Wed Mar 15, 2023 11:07 pm

Hi,
I performed an eigen analysis on a 2D elastic beam with fixed BCs. But the results differ significantly from those of abaqus. Is there anything wrong with the following code?
Best regards,

Code: Select all

import openseespy.opensees as ops
import numpy as np

ops.wipe()

# Create model
ops.model('basic', '-ndm', 2, '-ndf', 3)

# define the original nodes
ops.node(1,0,0)
ops.node(2,5,0)

ops.fix(1,1,1,1)
ops.fix(2,1,1,1)
ops.geomTransf('Linear', 1)


rho = 7850
A = 1
E = 2.1e11
Iz = 1
mass = rho*A
eleArgs = ['elasticBeamColumn', A, E, Iz,1, '-mass', mass]
ops.mesh('line', 1, 2, 1, 2, 0, 3, 0.2, *eleArgs)

num_modes = 10
eigenValues = ops.eigen('-fullGenLapack',num_modes) # calculate eigenvalues
freqs = [] # list to store frequencies
for i in range(num_modes):
    freq = (eigenValues[i])**0.5/(2*np.pi) # calculate frequencies from eigenvalues
    freqs.append([i+1, freq])
freqs = np.array(freqs) # convert freqs to an array

mhscott
Posts: 868
Joined: Tue Jul 06, 2004 3:38 pm
Location: Corvallis, Oregon USA
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Re: Eigenvalue analysis of a simple beam

Post by mhscott » Thu Mar 16, 2023 4:31 am

What frequencies do you expect out of Abaqus? Which frequencies are the correct theoretical solution?

devilmaycry
Posts: 6
Joined: Tue Feb 05, 2013 3:37 am
Location: Iran

Re: Eigenvalue analysis of a simple beam

Post by devilmaycry » Thu Mar 16, 2023 5:19 am

The list of frequencies (Hz) provided by abaqus is 292.59, 516.88, 545.88, 776.87, etc. whereas the results provided by opensees is 516.87, 736.68, 1031.72, 1542.49, etc.!
Last edited by devilmaycry on Thu Mar 16, 2023 9:29 am, edited 1 time in total.

mhscott
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Joined: Tue Jul 06, 2004 3:38 pm
Location: Corvallis, Oregon USA
Contact:

Re: Eigenvalue analysis of a simple beam

Post by mhscott » Thu Mar 16, 2023 5:39 am

What is the mode shape of the first mode (292.59 Hz) you get out of Abaqus?

devilmaycry
Posts: 6
Joined: Tue Feb 05, 2013 3:37 am
Location: Iran

Re: Eigenvalue analysis of a simple beam

Post by devilmaycry » Thu Mar 16, 2023 9:28 am

Dear Professor Scott,
It turns out that OpenSees had calculated the frequencies correctly all along!
Upon further investigation, I discovered that I had meshed my model in Abaqus using B21 and B22 elements (2-node linear beam and 3-node quadratic beam), which resulted in similar results when using the Elastic Timoshenko Beam Column Element in OpenSees. However, when I changed the elements in Abaqus to B23 (2-node cubic beam) elements, the results matched those provided by OpenSees using Elastic Beam Column Elements.
Best regards,

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