Free vibration analysis of composite plates by higher-order 1D dynamic stiffness elements and experiments

Abstract

A novel approach for free vibration analysis of composite plate-like structures is introduced in this paper. Refined beam theories are formulated by making use of the Carrera Unified Formulation (CUF). By exploiting the hierarchical characteristics of CUF, the differential equations of motions and the natural boundary conditions are written in a compact and concise form in terms of fundamental nuclei, whose formal mathematical expressions do not depend on the order of the theory N. After the closed form solution of the N-th order beam model is sought, a general procedure to derive the exact Dynamic Stiffness (DS) matrix is devised by relating the amplitudes of the harmonically varying loads to those of the responses. The global DS matrices of composite laminated plates are then used with reference to the algorithm of Wittrick and Williams to carry out free vibration analyses. The accuracy of the proposed methodology is verified through published literature, finite element solutions from the commercial code MSC/Nastran and experimental tests.