Orthogonal polynomials and sub-sectioning method for vibration of plates

Abstract

Flexural vibrations of plates with discontinuities in the form of cracks and cutouts are investigated using a computationally efficient and accurate numerical scheme; the scheme combines the flexibility of dividing the problem domain into appropriate segments and the high accuracy resulting from the use of orthogonal polynomial functions generated using the Gram-Schmidt process. The frequency parameters obtained for standard plate problems using the proposed method compare very favourably with existing numerical and analytical results. The scheme is then extended to new cases involving plates with cutouts and cracks subjected to various combinations of inner and outer edge conditions. © 1990.