Vibration of a Clamped Wedge

Description

Determine the fundamental frequency of the in plane vibration of a cantilever wedge-shaped plate. The plate has the dimensions shown in the figure. The dimensions of the wedge are as follows: t = 1 in, b = 2 in, L = 16 in.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Frequency_5.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 0.75".

Material Properties

Modulus of elasticity = 3 X 10⁷ psi, Density = 0.2812 lb/in³.

Results

The first in-plane natural frequency is calculated by: f₁ = (5.315 b/2πL²)*(E/3ρ)^1/2. Where E is the modulus of elasticity and ρ is the density.

Frequency No.	Theory (Hz)	SOLIDWORKS Simulation (Hz)
1	774.55	778.07

Reference

Timoshenko, S., and Young, D. H., “Vibration Problems in Engineering", 3rd Edition, D. Van Nostrand Co., Inc., New York, 1955, p. 392.