Boundary Control of Large Amplitude Vibration of Anisotropic Composite Laminated Plates

Abstract

This paper presents a solution to the stabilization problem of large amplitude vibration of the anisotropic composite laminated plates when the Kirchhoff theorem is used to model geometric equations of strain. Because of the large displacement in the normal direction to the plate, the plate displacements in in-plane directions are not dispensable, and strains and governing equations for transverse vibration and in-plane motions are nonlinear; therefore, the nonlinear boundary control method is proposed to be utilized to stabilize the plate vibration. The boundary control forces consist of feedback of the velocities and slope at the boundary of the plate. By applying the proposed method, it is possible to asymptotically stabilize large amplitude vibration of anisotropic composite plates with simply supported boundary conditions without resorting to truncation of the model and without the use of in-domain measuring and actuating devices.