4.5.6 Test 13H: Simply supported thin square plate: harmonic forced vibration

Product: ABAQUS/Standard

Elements tested

S3 S3R S4 S4R S4R5 S8R S8R5 S9R5 STRI3 STRI65 SC6R SC8R

Problem description

Material and geometry specifications are as given in “Test 13: Simply supported thin square plate: frequency extraction,” Section 4.5.5.

Forcing function:

Steady-state harmonic.

100 N/m² over whole plate.

0 to 4.16 Hz

Damping:

Response:

and at center of plate.

Gauss integration is used for the shell cross-section in input file nfh1368x.inp.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 13H from NAFEMS “Selected Benchmarks for Forced Vibration,” R0016, March 1993.

Response predicted by ABAQUS

Results and discussion

The results are given in Table 4.5.6–1 and Table 4.5.6–2. The values enclosed in parentheses are percentage differences with respect to the reference solution. The modal solutions are obtained from Step 2 in files whose names begin with nfm13.

Table 4.5.6–1 Modal solution.

	Peak displacement (mm)	Peak stress (N/mm²)	Frequency (Hz)
Reference solution	45.42	30.03	2.377
S4	45.03 (–0.85%)	31.33 (4.3%)	2.418 (–1.72%)
S4R	45.33 (–0.20%)	30.34 (1.03%)	2.410 (1.39%)
S4R5	45.42 (0.00%)	30.41 (1.27%)	2.407 (1.26%)
S8R	43.12 (–5.06%)	33.73 (12.32%)	2.441 (2.69%)
S8R5	45.50 (0.18%)	35.12 (16.95%)	2.377 (0.00%)

Table 4.5.6–2 Direct solution.

	Peak displacement (mm)	Peak stress (N/mm²)	Frequency (Hz)
Reference solution	45.42	30.03	2.377
S3/S3R	41.56 (–8.50%)	27.82 (–7.36%)	2.49 (4.75%)
S4	44.93 (–1.08%)	31.26 (4.10%)	2.420 (1.81%)
S4 (collapsed)	41.56 (–8.50%)	27.82 (–7.36%)	2.49 (4.75%)
S4R	45.38 (–0.09%)	30.37 (1.13%)	2.405 (1.18%)
S4R (collapsed)	41.56 (–8.50%)	27.82 (–7.36%)	2.49 (4.75%)
S4R5	45.41 (–0.02%)	30.39 (1.20%)	2.405 (1.18%)
S8R	43.86 (–3.43%)	34.31 (14.25%)	2.446 (2.90%)
S8R5	44.66 (–1.34%)	34.49 (14.85%)	2.385 (0.34%)
S9R5	44.59 (–1.83%)	32.24 (7.36%)	2.39 (0.55%)
STRI3	44.74 (–1.49%)	32.81 (9.26%)	2.36 (–0.71%)
STRI65	44.96 (–1.01%)	33.19 (10.5%)	2.36 (–0.71%)
SC6R	41.56 (–8.5%)	27.82 (–7.36)	2.49 (4.75%)
SC8R	45.38 (–0.09%)	30.37 (1.13%)	2.405 (1.18%)