Flexural vibration of polygonal plates : treatments of sharp re-entrant corners

The free vibrations of a class of polygonal plates with sharp re-entrant corners are investigated. A highly versatile and accurate domain decomposition method (DDM) is proposed for solutions. Frequency parameters and modes shapes of thin, isotropic plates having L-, T- and C-shapes planforms are computed. The L-shaped plate, in particular, is employed as the basic building element for the other configurations. In the preparatory stage of the solution process, this L-shaped element is subdivided into three smaller rectangular subdomains. Each subdomain is assigned with appropriate polynomial-based displacement shape function. Continuities in displacement, slope and higher derivatives between adjacent subdomains are enforced at the interconnecting edges. This results in a set of continuity matrices which are used to couple the respective strain and kinetic energies of each subdomain. A global energy functional which is the aggregate of the respective energy contributions from each subdomain is derived and minimized according to the Ritz principle to arrive at the linear eigenvalue equation for the complete plate domain. A comprehensive range of mode shapes is presented in contour plots. Also results of extensive parametric studies to investigate the effects of changing geometric parameters on the natural frequencies of the complex plates are presented.