A SINUSOIDAL STIFFNESS MATRIX FOR BUCKLING AND VIBRATION ANALYSES OF RECTANGULAR MINDLIN PLATES

Abstract

A sinusoidal stiffness matrix for buckling and vibration analyses of rectangular Mindlin plates has been derived. The buckling and/or vibration equations of Mindlin plate theory have been stated. It has been shown how these equations contain, as a limiting case, those of classical thin plate theory. The equations have been written in dimensionless form and the independent parameters which govern the problem have been established. The contributions of shear deformation and rotational inertia have been identified. Coupled terms, related to both shear deformation and rotational inertia, have also been noted. Some considerations for a proper choice of the shear factor have been reported on the basis of information available in the literature. Finally, it has been shown how the coefficients of the stiffness matrix arising from Mindlin plate theory may be related to those of the classical theory and convergence in the limit has been demonstrated. Some remarks on the aspects which need further investigation and development conclude the paper.