An analytical method of extension-twisting coupling vibration of piezoelectric composite laminates

This paper presents a dynamic analytical model of torsional vibration induced by extension-twisting coupling of anisotropic composite laminates with piezoelectric actuators by use of a non-conventional method (a reduced bending stiffness matrix). The aims of the method are not to require to find in-plane displacements in deriving equations of motion, and only to require to find an out-of-plane displacement of the laminate. Thus, the method changes a three-dimension problem into an one-dimension problem and none of structure complexities is lost. Finally, the model allows the analysis of anisotropic plate to be directly utilized. In addition, the Hamilton principle and the classical plate theory are used for the derivation of the model. The analytical solution of the model in the case of harmonic excitation is given. Some comparisons are presented with a finite element analysis (TEA) model. The analytical model is verified by FEA.