Three-dimensional vibration of rectangular plates: Variance of simple support conditions and influence of in-plane inertia

Plate models developed on the basis of the three-dimensional elasticity theory are crucial to the correct solutions in dynamics problems. In a three-dimensional setting, there exist numerous possible definitions of boundary conditions. This paper attempts to identify the variance of three-dimensional simple support conditions existing in practice. The hard simple support condition assumes vanishing normal stresses at the edges and zero transverse and tangential displacement at the peripheries. The soft simple support, on the other hand, imposes zero transverse displacement with vanishing normal and shear stresses at the boundaries. To quantify the relative effects of each boundary condition on the vibratory responses of thick plates, a global three-dimensional Ritz formulation is employed for analysis. This technique uses sets of finite polynomial series in Cartesian co-ordinates to approximate the global normal mode variations of the plate. These separable one-dimensional polynomials are orthogonally generated within the plate domain such that all the essential edge conditions are identically satisfied. The accuracy of the proposed three-dimensional Ritz method is assured from the convergence and comparison studies. Numerical experiments have been conducted to study firstly, the effects of geometric parameters on the overall normal mode characteristics of simply supported plates ; and secondly, the effects of in-plane inertia on the vibration frequencies of plates with different thicknesses. The three-dimensional deformed mode shapes for selected cases have also been computed. These have served to describe more vividly the normal mode characteristics of different types of simply supported rectangular plates. © 1994.