Vibration Analysis of Thin Plates Subject to Piezoelectric Actuation: A New Perspective in Modeling and Numerical Analysis

This paper undertakes model development and numerical simulations of vibration problem of piezoelectrically actuated thin plates with a holistic perspective. Constitutive laws governing piezoelectric actuator are integrated with the potential and kinetic energies of combined plate-actuator system. The equations of motions are derived using variational approach and verified with results obtained by Newton’s equilibrium approach. It is verified that the field coupled components associated with piezoelectric actuator appear as distributed moments over the area of the actuator. The equations of motion are solved using modal analysis deploying Raleigh Ritz method utilizing Boundary Characteristic Orthogonal Polynomials (BCOP). The shape functions generated using this method is used in Assumed Mode Method (AMM) to numerically simulate forced vibration analysis. Since Raleigh Ritz analysis with BCOP can be deployed with the plates of all the geometries, minor modifications in selecting the shape functions enables one to use the same method to calculate natural frequencies of annular plate as well.