Test 21R: Simply supported thick square plate: 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

S4

S4R

S4R5

S8R

STRI65

Problem description

Material and geometry specifications are as given in Test 21: Simply supported thick square plate: frequency extraction.

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. ζ=​ 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 δ PSD(mm2/Hz)Peak σ 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%)