Vibrations of an initially stressed transversely isotropic circular thick plate

Equations of motion for a transversely isotropic circular thick plate in a general state of nonuniform initial stress where the effects of transverse shear and rotary inertia are included are derived. The natural frequencies of axisymmetric clamped plates and simply supported plates subjected to initial stresses are investigated. The initial stress is taken to be a combination of a pure bending stress plus an extensional stress in the plane of the plate. These equations are solved by the Galerkin method. The effects of various parameters on the natural frequencies are studied.