Eigenvalue analysis of a simple beam

[devilmaycry]

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]

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

[devilmaycry]

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.!

[mhscott]

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

[devilmaycry]

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,