Vibratory characteristics of general laminates, I: symmetric trapezoids

This paper presents Part I of investigations of free flexural vibration of multi-layered symmetric and unsymmetric composite laminates with symmetric trapezoidal planform of arbitrary combinations of edge conditions. The Ritz procedure with pb-2 shape functions as the admissible functions is used to arrive at the governing eigenvalue equation. The set of pb-2 shape functions is intrinsically a product of a class of orthogonally generated two-dimensional polynomial functions and a basic function which ensures the satisfaction of geometric boundary conditions at the outset. Different boundary conditions, with various combinations of in-plane constraints, are considered. The effects of wide ranges of chord ratios, angles of fibre orientation and stacking sequences on the vibration response are investigated. With the aim of increasing the existing database, sets of previously unavailable vibration frequencies and mode shapes are presented as benchmarks for future reference.