Development of Fourier-p shape functions for vibration of plates

Abstract

A new approach is presented to incorporate the commonly well-behaved Fourier series with polynomials in representing the shape functions for vibration of plates using the Ritz Method. It significantly improves (i) <i>accuracy</i> and (ii) <i>convergence</i> of the common Ritz method using polynomials as shape functions. As polynomials tends to induce numerical instability, ill-conditioning and insolvability, the development of this Fourier-<i>p</i> Ritz approach helps to resolve these problems. Exhausting numerical computation can also be alleviated.