Product: ABAQUS/Standard
Material and geometry specifications are as given in “Test 13: Simply supported thin square plate: frequency extraction,” Section 4.5.5.
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. 
2%.
Response location:
Peak PSD of displacement and stress at center of plate.
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.
The results are shown in the following table. The values enclosed in parentheses are percentage differences with respect to the reference solution.
| Element type | Peak  PSD | Peak  PSD | Frequency |
|---|---|---|---|
| (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%) |
S4 elements, coarse mesh.
S4 elements, fine mesh.
S4R elements, coarse mesh.
S4R elements, fine mesh.
S8R5 elements, coarse mesh.
S8R5 elements, fine mesh.
STRI65 elements, coarse mesh.