Polynomial and harmonic differential quadrature methods for free vibration of variable thickness thick skew plates

Vibration analysis of skew fibre-reinforced composite laminated plates

A boundary element method is developed for the dynamic analysis of plates with variable thickness. The plate may have arbitrary shape and its boundary may be subjected to any type of boundary conditions. The non-uniform thickness of the plate is an arbitrary function of the coordinates x, y. Both free and forced vibrations are considered. The method utilizes the fundamental solution of the static problem of the plate with constant thickness to establish the integral representation for the deflection and, subsequently, by employing an efficient Gauss integration technique for domain integrals the equation of motion is derived as a discrete system of simultaneous ordinary differential equations with respect to the deflections at the Gauss integration nodal points. The equation of motion can be solved using the known techniques for multi-degrees of freedom systems. Numerical results are presented to illustrate the method and to demonstrate its efficiency and accuracy.

A BEM solution to dynamic analysis of plates with variable thickness

The analog equation method (AEM) is applied to dynamic analysis of plates with variable thickness. Both free and forced vibrations are considered. The fourth order partial differential equation with variable coefficients governing the dynamic response of the plate is converted to a quasi-static plate bending problem under a fictitious time dependent load. The fictitious load is established using the AEM. Numerical examples are presented which illustrate the efficiency and accuracy of the method.

M.M. Banerjee

Papers

On the vibration of skew plates of variable thickness