Parametric instability of conical shells by the generalized differential quadrature method

The parametric instability of truncated conical shells of uniform thickness under periodic edge loading is examined. The material considered is homoge neous and isotropic. This is the first instance that the Generalized Differ ential Quadrature (GDQ) method is used to study the effects of boundary con ditions on the parametric instability in shells. The formulation is based o n the dynamic version of Love's first approximation for thin shells. A form ulation is presented which incorporates the GDQ method in the assumed-mode method to reduce the partial differential equations of motion to a system o f coupled Mathieu-Hill equations. The principal instability regions are the n determined by Bolotin's method. Assumptions made in this study are the ne glect of transverse shear deformation, rotary inertia as well as bending de formations before instability. Copyright (C) 1999 John Wiley & Sons, Ltd.