Some Recent Advances in Linear and Nonlinear Dynamical Modeling of Elastic and Piezoelectric Plates

A previous review has covered our early efforts in dynamics and vibration of homogeneous and layered elastic plates and shells, including sandwiches. As an update, the present review summarizes our recent efforts in the same general area, now further including laminated composite and piezoelectric plates. These reflect the increasing importance of laminates, the growing interest in distributed active vibration control through the use of piezoelectric layers and often a combination of both. The main purpose of this paper is to again provide a systematic overview of linear and nonlinear dynamical modeling of both homogeneous and layered plates. As many of our contributions have been made by means of the variational equations of motion in three-dimensional elasticity and piezoelectricity, an extended discussion of these equations is included as an integral part of this review. Recent applications of these to the linear and nonlinear dynamical modeling of elastic laminates and piezoelectric layers are described.