Vibration of general triangular composite plates with elastically restrained edges

Triangular fibre reinforced composite plates are important structural elements in modern engineering structures. In this paper a computationally efficient and accurate numerical model is presented for the study of free vibration behaviour of anisotropic triangular plates with edges elastically restrained against rotation and translation. The approach developed is based on the Rayleigh–Ritz method and the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated using the Gram–Schmidt procedure. Several examples are solved and some results which correspond to particular cases are compared with existing values in the literature. New results are also presented for single layer composite plates with different fibre orientations and combinations of boundary conditions. For some plates, mode shapes of free vibration are also shown. Selected new transverse vibration mode shapes are presented to illustrate the effects of boundary constraints, aspect ratio and fibre orientation. The method can be applied to a wide range of elastic restraint conditions, any aspect ratio and for higher modes. The effect of the fibre orientation on the natural frequencies for plates with these restraint conditions are also considered.