Affordable Access

Publisher Website

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

Authors
Journal
Journal of Sound and Vibration
0022-460X
Publisher
Elsevier
Publication Date
Volume
284
Identifiers
DOI: 10.1016/j.jsv.2004.09.003

Abstract

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.

There are no comments yet on this publication. Be the first to share your thoughts.