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

Product: ABAQUS/Standard

Element tested

B32

Problem description

Material and geometry specifications are as given in “Test 5: Deep simply supported beam: frequency extraction,” Section 4.5.1.

Loading:

Uniform force of 1.0 applied to all elements, with white noise power spectral density of 1.E12 Pa²/Hz in the frequency region between 0/Hz and 1000/Hz, using the fully correlated type of random loading.

Damping:

16 modes with direct damping. 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 PSD	Peak PSD	Frequency
	(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%)

Input file

nfr5x32x.inp

B32 elements.