Vibration of an incompressible isotropic linear elastic rectangular plate with a higher-order shear and normal deformable theory

We use a mixed higher-order shear and normal deformable plate theory (HOSNDPT) of Batra and Vidoli with Poissonʹs ratio equal to 0.49 and the finite element method to analyze vibrations of a homogeneous isotropic rectangular plate made of an incompressible linear elastic material. Through-the-thickness integrals are evaluated exactly, and those over an element in the midplane of the plate are evaluated by using the 2 × 2 Gauss quadrature rule. The plate theory equations are used to ascertain frequencies of a clamped–clamped and a clamped–free square/rectangular plate of different aspect ratios. Through-the-thickness modes of vibration valid for compressible and incompressible materials and missed by previous investigators are also identified. Computed frequencies are found to match well with those deduced from the analytical solution.