Extensional vibrations of composite circular plates of moderate uniform thickness

Abstract

Mathematical treatment of such vibrations of plates which do not involve any transverse displacement of points in the middle plane goes back to Cauchy and Poisson. Present-day considerations are based upon the well-known approximate theory worked out by J. H. Michell (1900). Attention has been paid especially to isotropic circular plates, but solutions of problems relating to composite plates have not yet been obtained. The case of a uniform circular plate consisting of any finite number of homogeneous and isotropic concentric parts may serve as an example.