Exact Solutions for Free-Vibration Analysis of Rectangular Plates Using Bessel Functions

[+] Author and Article Information
Jiu Hui Wu, A. Q. Liu

School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore 639798

H. L. Chen

Institute of Vibration and Noise Control, Xi’an Jiaotong University, Xi’an 710049, China

J. Appl. Mech 74(6), 1247-1251 (Apr 23, 2005) (5 pages) doi:10.1115/1.2744043 History: Revised April 23, 2005; Received March 14, 2007

A novel Bessel function method is proposed to obtain the exact solutions for the free-vibration analysis of rectangular thin plates with three edge conditions: (i) fully simply supported; (ii) fully clamped, and (iii) two opposite edges simply supported and the other two edges clamped. Because Bessel functions satisfy the biharmonic differential equation of solid thin plate, the basic idea of the method is to superpose different Bessel functions to satisfy the edge conditions such that the governing differential equation and the boundary conditions of the thin plate are exactly satisfied. It is shown that the proposed method provides simple, direct, and highly accurate solutions for this family of problems. Examples are demonstrated by calculating the natural frequencies and the vibration modes for a square plate with all edges simply supported and clamped.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Vibration mode functions with n=2 and m=1 for a fully simply supported plate at different nondimensional natural frequencies: (a)ka=3.6744 and (b)ka=10.1215

Grahic Jump Location
Figure 2

Vibration mode functions with n=6 and m=3 for a fully simply supported plate at different nondimensional natural frequencies: (a)ka=9.7066 and (b)ka=12.9751

Grahic Jump Location
Figure 3

Vibration mode functions with n=4 and m=2 for a fully clamped square plate at different nondimensional natural frequencies: (a)ka=12.4022 and (b)ka=15.5795




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