EFFECT OF INITIAL CURVATURE ON NATURAL FREQUENCY OF THIN-PLATE ON HINGE SUPPORTS

This study investigates the influence of initial curvature on the dyna mic behavior of a hinge-supported thin plate. The large-deflection the ory is used to determine the mid-plane forces produced by the deflecti on and the initial curvature. Then, the vertical components of the mid -plane forces are found as a set of distributive surface loads applied on the plate in the transverse direction. Subsequently, the equilibri um condition of the plate is expressed in a nonlinear differential equ ation. With proper simplification and linearization the differential e quation leads to a special type of eigenvalue problem that can be solv ed by using a weighted residual method. Hence, the natural frequencies and modes are found. The computational results of examples clearly de monstrate the phenomenon of the natural frequencies moving upward when the plate is preformed into the shape of a specific mode of vibration .