Test 13R: Simply supported thin 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

S8R5

STRI65

Problem description

Material and geometry specifications are as given in Test 13: Simply supported thin square plate: frequency extraction.

Loading:

Uniform pressure of 1.0 applied to all elements, with white noise power spectral density of 10000 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 13R from NAFEMS “Selected Benchmarks for Forced Vibration,” R0016, September 1993.

 Peak δ PSDPeak σ PSDFrequency
 (mm2/Hz)[(N/mm2)2/Hz](Hz)
Reference solution 2063.20 1025.44 2.377

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.

Element typePeak δ PSDPeak σ PSDFrequency
(Mesh Size)(mm2/Hz)[(N/mm2)2/Hz](Hz)
S4 (4 × 4) 1901.8 (−7.8%) 844.25 (−17.67%) 2.549 (7.24%)
S4 (8 × 8) 2028.6 (−1.68%) 981.39 (−4.30%) 2.417 (1.68%)
S4R (4 × 4) 2040.2 (−1.11%) 665.98 (−35.05%) 2.5043 (5.36%)
S4R (8 × 8) 2062.2 (−0.05%) 923.83 (−9.91%) 2.4079 (1.30%)
S8R5 (4 × 4) 2071.5 (−0.40%) 1201.83 (17.2%) 2.3759 (−0.05%)
S8R5 (8 × 8) 2064.9 (0.08%) 1011.33 (−1.38%) 2.3767 (−0.01%)
STRI65 (2 × 4 × 4) 1989.4 (−3.58%) 942.13 (−8.14%) 2.4028 (1.09%)