Eigenvalue analysis of doubly connected plates with different configurations

This paper deals with the vibration and buckling analyses of the first-order shear deformable rhombic and square plates using a p-type variational method. The formulation includes rotary inertia and transverse shear terms. The full plate is modeled with a single domain defined by a set of geometric points in the plane of the plate. Square and rectangular plates with a circular hole at the center are treated as the numerical example for the doubly connected plate and are modeled using one quarter of the geometry and only two elements. The symmetry about x and y axes with regards to load and boundary conditions are exploited. Buckling coefficients and natural frequencies are calculated and compared with results from the published sources and the finite element method.