Effect of Initial Curvature on Natural Frequency of Thin Plate on Hinge Supports

Abstract

This study investigates the influence of initial curvature on the dynamic behavior of a hinge‐supported thin plate. The large‐deflection theory is used to determine the mid‐plane forces produced by the deflection 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 equilibrium condition of the plate is expressed in a nonlinear differential equation. With proper simplification and linearization the differential equation leads to a special type of eigenvalue problem that can be solved by using a weighted residual method. Hence, the natural frequencies and modes are found. The computational results of examples clearly demonstrate the phenomenon of the natural frequencies moving upward when the plate is preformed into the shape of a specific mode of vibration.