Modeling of torsional vibration induced by extension-twisting coupling of anisotropic composite laminates with piezoelectric actuators

In this paper we present a dynamic analytical model for the torsional vibration of an anisotropic piezoelectric laminate induced by the extension-twisting coupling effect. In the present approach, we use the Hamilton principle and a reduced bending stiffness method for the derivation of equations of motion. As a result, the in-plane displacements are not involved and the out-of-plane displacement of the laminate is the only quantity to be calculated. Therefore, the proposed method turns the twisting of a laminate with structural coupling into a simplified problem without losing its features. We give analytical solutions of the present model with harmonic excitation. A parametric study is performed to demonstrate the present approach.