4.5.5 Test 13: Simply supported thin square plate: frequency extraction

Product: ABAQUS/Standard  

Element tested

S8R5   

Problem description

Model:

Plate thickness = 0.05 m.

Material:

Young's modulus = 200 GPa, Poisson's ratio = 0.3, density = 8000 kg/m3.

Boundary conditions:

at all nodes. along all four edges. along edges and , along edges and .

Frequency extraction is performed in Step 1.

Reference solution

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

Mode shapes predicted by ABAQUS

The contour plots were generated by setting the maximum and minimum contour levels close to zero. Where contour levels coincided with the element boundaries, the maximum contour level was increased and the minimum contour level was decreased appropriately.

Results and discussion

The results are shown in the following table.

ModeABAQUS resultNAFEMS reference result% Difference
12.3772.3770.00
2, 35.9615.9420.32
49.4839.507–0.25
5, 612.13311.8842.10
7, 815.64015.4491.24

Input file

nfm1358x.inp

S8R5 elements.