4.5.10 Test 21H: Simply supported thick square plate: harmonic forced vibration

Product: ABAQUS/Standard

Elements tested

S3 S3R S4 S4R S4R5 S8R S8R5 S9R5 STRI3 STRI65

Problem description

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

Forcing function:

Steady-state harmonic.

1 MN/m² over whole plate.

0 to 78.17 Hz

Damping:

Response:

and at center of plate.

The modal solution is obtained from Step 2 in files whose names begin with nfm21.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 21H from NAFEMS “Selected Benchmarks for Forced Vibration,” R0016, March 1993.

Response predicted by ABAQUS

Results and discussion

The results are given in Table 4.5.10–1 and Table 4.5.10–2. The values enclosed in parentheses are percentage differences with respect to the reference solution.

Table 4.5.10–1 Modal solution.

	Peak displacement (mm)	Peak stress (N/mm²)	Frequency (Hz)
Reference solution	58.33	800.8	45.90
S4	59.54 (2.03%)	784.01 (–2.09%)	46.67(1.68%)
S4R	60.01 (2.88%)	760.4 (–5.04%)	46.52 (1.35%)
S4R5	59.93 (2.74%)	760.8 (–5.00%)	46.51 (1.33%)
S8R	59.94 (2.76%)	880.1 (9.90%)	45.94 (0.09%)

Table 4.5.10–2 Direct solution.

	Peak displacement (mm)	Peak stress (N/mm²)	Frequency (Hz)
Reference solution	58.33	800.8	45.90
S3/S3R	57.52 (–1.39%)	745.7 (–6.88%)	47.92 (4.40%)
S4R (collapsed)	57.52 (–1.39%)	745.7 (–6.88%)	47.92 (4.40%)
S4 (collapsed)	57.52 (–1.39%)	745.7 (–6.88%)	47.92 (4.40%)
S4	60.77 (4.18%)	800.3 (–0.06%)	46.76(1.87%)
S4R	61.33 (5.14%)	776.9 (–2.98%)	46.39 (1.07%)
S4R5	61.09 (4.73%)	775.7 (–3.13%)	45.98 (0.17%)
S8R	61.87 (6.07%)	908.4 (13.44%)	45.98 (0.17%)
S8R5	60.81 (4.25%)	887.8 (10.8%)	46.0 (0.22%)
S9R5	60.73 (4.11%)	830.3 (3.68%)	46.0 (0.22%)
STRI3	55.88 (–4.20%)	818.4 (2.19%)	46.8 (1.96%)
STRI65	62.47 (7.09%)	860.7 (7.48%)	46.0 (0.22%)