Vibration of Continuous Systems, 2nd Edition

14Transverse Vibration of Plates

14.1 INTRODUCTION

A plate is a solid body bounded by two surfaces. The distance between the two surfaces defines the thickness of the plate, which is assumed to be small compared to the lateral dimensions, such as the length and width in the case of a rectangular plate and the diameter in the case of a circular plate. A plate is usually considered to be thin when the ratio of its thickness to the smaller lateral dimension (such as width in the case of a rectangular plate and diameter in the case of a circular plate) is less than . The vibration of plates is important in the study of practical systems, such as bridge decks, hydraulic structures, pressure vessel covers, pavements of highways and airport runways, ship decks, airplanes, missiles, and machine parts. The theory of elastic plates is an approximation of the three‐dimensional elasticity theory to two dimensions, which permits a description of the deformation of every point in the plate in terms of only the deformation of the midplane of the plate. The equations of motion of plates are derived using the thin plate theory as well as the Mindlin theory, which considers the effects of rotary inertia and shear deformation. Free and forced vibration of rectangular and circular plates are considered. The vibration of plates with variable thickness, of plates on elastic foundation, and of plates ...