VM151

VM151
Nonaxisymmetric Vibration of a Circular Plate

Overview

Reference:	R. J. Blevins, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Co., New York, NY, 1979, pg. 240, no. 2.
Analysis Type(s):	Mode-frequency Analysis (ANTYPE = 2)
Element Type(s):	Axisymmetric-Harmonic Structural Shell Elements (SHELL61)
Input Listing:	vm151.dat

Test Case

A circular plate with a simply supported edge is allowed to vibrate freely. Determine the natural frequencies f_i,j for the first mode of vibration (j = 1 = no. of nodal circles, including the boundary) for the first three harmonics (i = 0,1,2 = no. of harmonic indices).

Figure 211: Circular Plate Problem Sketch

Material Properties

Geometric Properties

E = 30 x 10⁶ psi

υ = 0.3

ρ = 0.00073 lb-sec²/in⁴

a = 3 in

t = 0.05 in

Analysis Assumptions and Modeling Notes

Poisson's ratio defaults to 0.3 and is not defined with the input data. A total of 9 elements is selected for meshing. Modal analysis is solved using Block-Lanczos eigensolver.

Results Comparison

	Target	Mechanical APDL	Ratio
f_o,1, Hz	269.96	267.67	0.992
f_1,1, Hz	756.13	753.74	0.997
f_2,1, Hz	1391.3	1388.89	0.998

Figure 212: Mode Shape Displays

Window 1 - f_0,1; Window 2 - f_1,1; Window 3 - f_2,1