Asymmetric thermo-inertial buckling of annular plates

The present research deals with the nonaxisymmetric buckling behaviour of isotropic homogeneous annular plates subjected to simultaneous effects of uniform temperature rise and constant angular speed. First-order shear deformation plate theory is used to obtain the complete set of governing equations and the associated boundary conditions. Pre-buckling deformations and stresses of the plate are obtained using the solution of a plane stress formulation, neglecting the rotations and lateral deflection. Applying the adjacent equilibrium criterion, the linearised stability equations are obtained. The resulting equations are solved using a hybrid method, including the exact trigonometric functions through the circumferential direction and generalised differential quadrature method through the radial direction. The resulting eigenvalue problem is solved to obtain the critical conditions of the plate and the associated circumferential mode number. Numerical results reveal that, only for annular plates with exterior edge clamped, rotation may enhance the critical buckling temperature of a plate under special circumstances. Furthermore, asymmetric stability analysis should be performed to extract the critical state and buckled shape of a rotating annular plate subjected to uniform heating. Otherwise, the critical buckling temperature is overestimated and the buckling pattern is wrongly predicted.