Lekhnitskii's classic formula serving as an exact mode shape of simply supported polar orthotropic inhomogeneous circular plates

Author Type

Faculty

Co-Author Type 1

Faculty

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

The semi-inverse problem of free vibration of simply supported inhomogeneous polar orthotropic plates is studied. The mode shape is postulated in the form of the classic formula by Lekhnitskii, namely, the static deflection of the associated uniform polar orthotropic circular plate under uniform loading. The ratios of the circumferential rigidity to the radial rigidity are identified as integer numbers, so that the candidate mode shapes constitute the polynomial functions. The flexural rigidities themselves are also represented by polynomials. The semi-inverse problem of identifying the coefficients of the flexural rigidities is solved analytically. It appears remarkable, that for numerous cases the simple method developed in this study provides novel closed form solutions for the design of the polar orthotropic circular plates with pre-specified mode shapes. © 2005 Elsevier Ltd. All rights reserved.

First Page

1239

Last Page

1254

DOI

10.1016/j.jsv.2005.06.039

Publication Date

4-4-2006

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