Test 5R: Deep simply supported beam: random forced vibration

This problem provides evidence that Abaqus can reproduce the result from the benchmark defined by NAFEMS and cited as the reference solution.

This page discusses:

ProductsAbaqus/Standard

Elements tested

B32

Problem description

Material and geometry specifications are as given in Test 5: Deep simply supported beam: frequency extraction.

Loading:

Uniform force of 1.E6 N/m applied to all elements with unit white noise power spectral density in the frequency region between 0 Hz and 1000 Hz, using the fully correlated type of random loading.

Damping

16 modes with direct damping. ζ=​2%.

Response

Peak PSD of displacement and stress.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 5R from NAFEMS “Selected Benchmarks for Forced Vibration,” R0016, September 1993.

Results and discussion

The results are shown in the following table. The values enclosed in parentheses are percentage differences with respect to the reference solution.

 Peak δ PSDPeak σ PSDFrequency
 (mm2/Hz)[(N/mm2)2/Hz](Hz)
Reference solution 180.90 58516 42.65
Abaqus solution 181.75 (0.47%) 56926 (−2.72%) 42.66 (0.12%)