Free Vibration of a Rectangular Plate Supported on the Sides and Some Segments

Abstract

A theoretical method of analysis is presented for the study of the free vibration of a rectangular plate supported on the sides and elastically supported on some segments parallel to the sides. Applying the method to (1) a rectangular plate simply supported on the sides and elastically supported on a cross-shaped support located in the center of the plate and (2) a rectangular plate clamped on the sides and a rectangular support inside the plate, the equations for determining the natural frequencies and the mode shapes of the symmetrical and antisymmetrical vibration of such plates are derived. And the results of the numerical calculation carried out by the use of these equations are presented in some figures.