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 homogeneous and isotropic. This is the Þrst instance that the Generalized Di¤erential Quadrature (GDQ) method is used to study the e¤ects of boundary conditions on the parametric instability in shells. The formulation is based on the dynamic version of LoveÕs Þrst approximation for thin shells. A formulation is presented which incorporates the GDQ method in the assumed-mode method to reduce the partial di¤erential equations of motion to a system of coupled MathieuÐHill equations. The principal instability regions are then determined by BolotinÕs method. Assumptions made in this study are the neglect of transverse shear deformation, rotary inertia as well as bending deformations before instability. Copyright