An unusual exact, closed-form solution for axisymmetric vibration of inhomogeneous simply supported circular plates
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
Recommended Citation
Elishakoff, Isaac and Storch, Joel A., "An unusual exact, closed-form solution for axisymmetric vibration of inhomogeneous simply supported circular plates" (2005). Faculty Scholarship. 424.
https://digitalcommons.fau.edu/faculty_papers/424