Transverse Vibration of Thick Annular Sector Plates

Abstract

This paper investigates the free vibration of thick sector plates with different supporting edge conditions. The Rayleigh‐Ritz procedure is used in the energy functional, which includes the effect of shear deformation and rotatory inertia in deriving the governing eigenvalue equation. Sets of mathematically complete two‐dimensional polynomials (P‐2) are used as the admissible displacement and rotational functions. A basic function (B) is introduced to satisfy the prescribed free, simply supported and clamped supporting edge conditions. This resulting PB‐2 Rayleigh‐Ritz method is applied to obtain solutions for thick sector plates of different radii (cutout ratios), sector angles, relative thickness ratios and with various end conditions along the radial and circumferential edges. The present results, wherever possible, are compared with existing published values from the open literature.