Simply Supported Rectangular Plate with In-plane Pressure

Description

Obtain the fundamental frequency of a 40"X40"X1" simply supported square plate subjected to an in-plane pressure of 33.89 psi as shown in the figure.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Frequency_6.SLDPRT and open the file.

Study Type

Frequency.

Mesh Type

Shell mesh.

Shell Parameters

Shell thickness = 1 in - Thin formulation.

Meshing Parameters

Use a Global Size of 7.5".

Material Properties

Modulus of elasticity = 3 X 10⁴ psi, Poisson's ratio = 0.3, Density = 0.1158 lb/in³.

Modeling Hints

The Intel Direct sparse solver is used with the Use soft spring to stabilize model option turned on.

Results

Frequency No.	Theory (Hz)	SOLIDWORKS Simulation (Hz)
1	4.20	4.004

The study WithoutLoad shows the fundamental frequency to be 5.93 Hz when the compressive load is not considered. Compressive loads lower the natural frequencies.

Reference

Leissa, A.W., “Vibration of Plates,” NASA SP-160, p. 277.