Transverse vibration of thick rectangular plates—IV. Influence of isotropic in-plane pressure

Abstract

Part IV of this series of four papers reports a study of the effects of isotropic in-plane pressure on the vibration response of thick rectangular plates. In the theoretical formulation of the governing functional, the effects of transverse shear deformation and rotatory inertia have been incorporated using Mindlin's first order shear deformation theory. Sets of mathematically complete two-dimensional polynomials have been used as the admissible displacement and rotation functions in the Rayleigh-Ritz procedure to derive the governing eigenvalue equation. In this paper, several rectangular plates with different combinations of boundary conditions and various aspect ratios a b and relative thickness ratios t b are considered. Sets of reasonably accurate vibration frequencies are presented for these in-plane loaded rectangular plates in the form of design charts. The results, where possible, are compared with established values from the open literature. Some basic discussion of the effects of shear deformation and rotatory inertia has been included based on trends in the numerical results.