VIBRATION OF THICK AND SANDWICH PLATES

Abstract

This research study consists of two parts. In the first part, we consider the free vibration problem of isotropic, thick plates, of general polygonal shape and simply supported edges. Complicating effects such as the presence of initial stresses and a Winkler-Pasternak foundation are also considered. Based on an analogy approach, exact vibration relationships between classical and shear deformable theories are developed. The relationships allow one to obtain readily the shear deformable plate frequencies from well known and abundant classical vibration solutions.

In the second part, we consider the free vibration problem of skew sandwich plates composed of an orthotropic core and laminated facings. To solve the vibration problem, the Rayleigh-Ritz method has been adopted. Proposed herein is a set of Ritz functions consisting of the product of mathematically complete, polynomial functions and the boundary equations raised to appropriate powers. With these Ritz functions, the Rayleigh-Ritz method can be automated to handle such composite plates with any combination of edge conditions. For convenience and better accuracy, the Ritz formulation was derived in the skew coordinate system. Vibration frequencies of rectangular plates (a special case of skew plates) obtained via this method have been found to be in good agreement with previous researchers' results: Parametric studies were also carried out to determine the effects of laminated facings, core's bending, skew angles, fibre orientations and thickness of plates on the vibrational behaviour of skew sandwich plates. Extensive frequency parameters have been tabulated for researchers and engineers who are designing such skew sandwich plates.