Product: ABAQUS/Standard
The tests in this section verify the random response capability for structures subjected to correlated and uncorrelated excitations. The tests include excitation from base motion and from concentrated and distributed loads.
A two-element cantilever beam aligned along the 
-axis is excited by prescribed ground accelerations in global degrees of freedom 1 and 6. B21 elements of unit length are used. A white noise power spectral density is used to describe the applied ground accelerations.
Since random response analysis is a modal-based procedure, a *FREQUENCY step is required to obtain the mode shapes and natural frequencies of the system. Steps 2 and 3 test correlated and uncorrelated excitation between global degrees of freedom 1 and 6, respectively. Steps 4 and 5 test arbitrary load case numbering. Only the first two mode shapes have been used in the *RANDOM RESPONSE steps, with a damping ratio of 0.01 for each mode.
For this problem the response power spectral densities can be relatively easily evaluated by hand calculations. The power spectral densities at various frequencies (including the natural frequencies) agree with the hand calculations. The results for Steps 2 and 4 should be identical to each other, as should the results for Steps 3 and 5.
Correlated and uncorrelated random concentrated loads.
Multiple *PSD-DEFINITIONs, *CORRELATIONs, and LOAD CASEs.
A two-element cantilever beam aligned along the 
-axis is excited by transverse distributed and concentrated loads. The concentrated loads are applied at the free end (magnitude of –1.0) and at the midnode (magnitude of –2.0). The distributed load acts on the element closest to the cantilevered end (magnitude of 4.0). B21 elements of unit length are used. Both the distributed load and the concentrated loads are described by white noise power spectral densities.
Since random response analysis is a modal-based procedure, a *FREQUENCY step is required to obtain the mode shapes and natural frequencies of the system. Steps 2 and 3 test correlated and uncorrelated *CLOADs, respectively. Steps 4 and 5 test arbitrary load case numbering. Only the first two mode shapes have been used in the *RANDOM RESPONSE steps, with a damping ratio of 0.01 for each mode.
For this problem the response power spectral densities can be relatively easily evaluated by hand calculations. The power spectral densities at various frequencies (including the natural frequencies) agree with the hand calculations. The results for Steps 2 and 4 should be identical to each other, as should the results for Steps 3 and 5.