In the present investigation, the dynamic instability regions of shear deformable cross-ply laminated and composite cylindrical panels subjected to periodic nonuniform in-plane loads are reported. Since the applied in-plane load is nonuniform, initially the static part of the nonuniform in-plane loads are applied and the stresses (σx, σy and τxy) within the panel are evaluated by the solution of cylindrical panel membrane problem. Subsequently, superposing the stress distribution due to static and dynamic in-plane loads, the stress distributions within the panel are obtained. Using these stress distributions the governing equations of the problem are derived through Hamilton's variational principle based on higher-order shear deformation theory of elastic shell theory incorporating von Kármán-type nonlinear strain displacement relations. The governing partial differential equations are reduced into a set of ordinary differential equations (Mathieu-type of equations) by employing Galerkin's method. The instability boundaries of Mathieu equation corresponding to periodic solutions of period T and 2T are determined using Fourier series. Effect of various parameters like static and dynamic load factors, aspect ratio, thickness-to-radius ratio, shallowness ratio, linearly varying in-plane load, parabolic in-plane load and various boundary conditions on the instability regions are investigated.
