A DIFFERENTIAL QUADRATURE ANALYSIS OF VIBRATION FOR RECTANGULAR STIFFENED PLATES

Abstract Structures consisting of thin plates stiffened by a system of ribs or diaphragms form a class of structural elements of practical importance in various engineering applications. A differential quadrature analysis of free vibration of plates with eccentric stiffeners is presented. The plate and the stiffeners are treated separately. Simultaneous governing differential equations are derived from the plate dynamic equilibrium, the stiffener dynamic equilibrium, and equilibrium and compatibility conditions along the interface of a plate segment and a stiffener. The plate and the stiffeners have displacements in three dimensions. Shear forces and in-plane forces in the plate are considered to satisfy the compatibility at the interface of a plate segment and a stiffener. Meanwhile, in-plane inertia effects in the plate and in the stiffener are ignored. The application of the differential quadrature method is demonstrated by three examples: a simply supported plate with central eccentric stiffener, a clamped square plate with central eccentric stiffener, and a double-ribbed plate with all edges clamped. The natural frequencies are compared with the experimental results, and with the results obtained by finite element analysis. Very good agreement was found.