4.5.12 Test 21R: Simply supported thick square plate: random forced vibration

Product: ABAQUS/Standard

Elements tested

S4 S4R S4R5 S8R STRI65

Problem description

Material and geometry specifications are as given in “Test 21: Simply supported thick square plate: frequency extraction,” Section 4.5.9.

Loading:

Uniform pressure 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 location:

Peak PSD of displacement and stress at center of plate.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 21R 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(mm²/Hz)	Peak PSD[(N/mm²)²/Hz]	Frequency(Hz)
Reference solution	3401.81	641200	45.90
S4	3546.78 (4.26%)	614460 (–4.17%)	46.65 (1.63%)
S4R	3599.92 (5.82%)	—	46.51 (1.33%)
S4R5	3593.22 (5.63%)	—	46.50 (1.31%)
S8R	3594.31 (5.66%)	—	45.92 (0.04%)
STRI65	3712.97 (9.15%)	—	45.868 (–0.07%)

Input files

S4 elements.

S4R elements.

S4R5 elements.

S8R elements.

STRI65 elements.