Three-dimensional elasticity solutions for free vibrations of circular plates: a polynomials-Ritz analysis

This paper presents accurate three-dimensional elasticity solutions for fre e vibration of circular plates. The derivation of a linear frequency equati on based on an exact three-dimensional, small-strain, linearly elastic prin ciple is detailed. The solution to this problem is made possible by using t he Ritz method with a set of orthogonal polynomial series to approximate th e spatial displacements of the circular plate in cylindrical polar coordina tes. The perturbation of frequency responses due to the variations of bound ary conditions and thickness is investigated. First known frequency paramet ers and three-dimensional deformed mode shapes are presented in vivid graph ical forms. The accuracy of these results are verified by appropriate conve rgence studies and, when possible, are checked with existing solutions. (C) 1999 Elsevier Science S.A. All rights reserved.