An unusual exact, closed-form solution for axisymmetric vibration of inhomogeneous simply supported circular plates

Author Type

Faculty

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Journal of Sound and Vibration

Publication Status

Version of Record

Abstract

Apparently for the first time in the literature, an exact closed-form solution is derived for an axisymmetrically vibrating inhomogeneous circular plate that is simply supported at its boundary. The solution is characterized here as an unusual one since for its counterpart - the homogeneous plate, transcendental functions are called for whereas here a solution is found in elementary functions, namely, polynomials. The analysis is based on an inverse vibration problem: Given a candidate mode shape and density distribution, we calculate the plate stiffness so that the governing equation for the plate mode shape is identically satisfied. We also are able to obtain the expression for the corresponding natural frequency. © 2004 Elsevier Ltd. All rights reserved.

First Page

1217

Last Page

1228

DOI

10.1016/j.jsv.2004.09.003

Publication Date

6-21-2005

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