An Accurate Two-Dimensional Theory of Vibrations of Isotropic, Elastic Plates

An infinite system of two-dimensional equations of motion of isotropic elastic plates and edge and corner conditions are deduced from the three-dimensional equations of elasticity by expansion of displacement in a series of trigonometrical functions and a linear function of the thickness coordinate of the plate. The linear term in the expansion is to accommodate the in-plane displacements induced by the rotation of the plate normal in low-frequency flexural motions. A system of first-order equations of flexural motions and accompanying boundary conditions are extracted from the infinite system. It is shown that the present system of equations is equivalent to the Mindlin´s first-order equations, and the dispersion relation of straight-crested waves of present theory is identical to that of the Mindlin´s without introducing any corrections. Reduction of present equations and boundary conditions to those of classical plate theories of flexural motions is also presented