Frame eigenvalue problem

Image of frame

Objective

To verify the dynamic behavior of the beam elements in frequency analysis.

Problem description

A 9-story high and 10-bay long plane frame in [1] was analyzed (see figure). The data for the model are: E=432000, mass density=1.0, for all beams and columns A=3, I1=I2=I3=1.0 (units: ft, kips). The geometry and properties are as described here. The above Figure shows the model to be analyzed.

Finite element model

The finite element model consists of 189 2-node beam elements. The element matrices are evaluated in a closed form and the mass is represented in a lumped mass matrix. The subspace iteration method of frequency analysis is used. The first three eigenvalues are computed.

Plane frame eigenvalue problem: the first three modes
Image of the modelImage of the 1st mode
The modelFirst mode
Image of the 2nd modeImage of the 3rd mode
Second modeThird mode

Solution

The three first eigenvalues, calculated here, are compared to those calculated by FEEA SDK:

Calculated eigenvalues
Mode FEEA Reference
10.5895410.589541
25.526965.52695
31.658791.65878

Conclusion

The results obtained with FEEA SDK show an excellent comparison with the solution in this reference.