ON THE FREE-VIBRATION OF THIN ISOTROPIC AND RECTANGULARLY ORTHOTROPIC PLATES INVOLVING CURVED BOUNDARIES

The Rayleigh-Ritz method is used, with simple polynomials as the admissible functions, to obtain an eigenvalue equation for the free vibration of thin, flat plates which involve curved boundaries defined by polynomial expressions. The approach is used to determine the natural frequencies of several example plates including annular, circular, elliptical and hypocycloidal plates of isotropic and rectangularly orthotropic material. A plate with a more general curved boundary is also considered. © 1993 Academic Press Limited.