Abstract:

A finite element formulation for the vibration of a laminated plate including elastic, viscoelastic, and piezoelectric layers is presented. The model takes into account the mass, stiffness, and damping of each layer. A simplified discrete-layer plate theory and Hamilton's principle are used to formulate the equation of motion of the system. The continuity of the transverse stresses and the displacements are imposed at interlaminar layer interfaces. Only five degrees of freedom per node are necessary to describe the deformation of the plate. The discrete element is a quadrilateral shape with eight nodes and a total of 40 degrees of freedom. Extensional, bending, and transverse shear deformation are included in the formulation. One additional voltage degree of freedom per element is necessary for each piezoelectric layer. This finite-element formulation can be used to modelize the dynamic as well as the static response of a multilayered isotropic plate subjected to both mechanical and electrical excitations. The multilayer elastic--viscoelastic--piezoelectric element formulation will ultimately be used to study smart structures integrating piezoelectric layers acting as distributed actuators and sensors. Comparison with published experimental, analytical, and numerical results will be presented to validate the model.