Spectral modeling of vibrating plates with general shape and general boundary conditions

Abstract

The analysis and design of lightweight plate structures require efficient computational tools, because exact analytical solutions for vibrating plates are currently known only for some standard shapes in conjunction with a few basic boundary conditions. This paper deals with vibration analysis of Kirchhoff plates of general shape with non-standard boundary conditions, adopting a Rayleigh-Ritz approach. Three different coordinate mappings are considered, using different kinds of functions: 1) trigonometric and polynomial interpolation functions for mapping the shape of the plate, 2) trigonometric and polynomial interpolation functions for mapping a constraint domain of general shape, 3) products of linearly independent eigenfunctions evaluated from a standard beam in flexural vibration for describing the transverse displacement field of the plate. Flexural free vibration analysis of different shaped plates is then performed using the same approach: skew, trapezoid and triangular plates, plates with parabolic curved edges, sectors of circular plates, circular and elliptic annular plates. Purely elastic plates are considered, but the method may also be applied to the analysis of viscoelastic plates. The results are compared with those available in the literature and using standard finite element analysis.