Vibration analysis of arbitrarily shaped plates using beam characteristic orthogonal polynomials in the semi-analytical finite strip method

Abstract

A semi-analytical finite strip method mapping arbitrarily shaped plates into a natural co-ordinate plane using Serendipity functions is presented. The product of normalized beam characteristic orthogonal polynomials and Hermitian polynomials form the displacement function for the strip in the natural co-ordinate domain. Flexural free vibration analysis of various shaped plates is performed. Results show that as long as the plate is modelled by high enough degree mapping functions for the specific applications requested, the flexural frequencies obtained are in excellent agreement with those found in the literature.