Comparison of experiments with finite element analysis of plates with piezoelectric sensors/actuators

A finite element formulation is developed including the fully coupled electrical-structural constitutive relations. An effort has been made to develop the most general formulation applicable to laminated composite plates with inclusion of piezoceramic sensors/actuators. To this end, the von Karman large deflection theory was included, due to the results obtained from the experiments conducted. Solution of the large deflection problem lead to an electrical-structural coupled tangent stiffness, which is believed to be the first time reported in the literature. This paper presents comparison of the finite element simulation to experimental results for both static and dynamic piezoceramic sensors in addition to dynamic piezoceramic actuation. INTRODUCTION Piezoelectric material maintains a complex and intricate relationship between several physical sciences such as materials, thermal, electric fields, and elasticity. Evidence of the piezoelectric's complexity can be demonstrated by the seemingly continuous research conducted since its discovery in 1880 by Pierre and Jaques Curie. Much of the research set out to determine analytical models describing the piezoelectric phenomenon and lead to discrete devices such as extremely sharp crystal filters and stable oscillators. Mindlin developed classical methods describing the analysis on waves and vibrations in isotropic elastic plates concurrently with high frequency vibration of crystal plates. Allik and Hughes developed a solid, or three dimensional, finite element to model transducers and crystal oscillators. However, given that smart structures typically consist of thin piezoelectric layers attached to structures that are several orders of magnitude greater in thickness, the solid finite element formulation leads to an inherently inefficient process in which to model the complete physical structure. Subsequently Tzou and Tseng * Graduate Student, Student member AIAA. t Professor, Associate Fellow AIAA. "This paper is declared a work of the U.S. Government and is not subject to copy right protection in the United States." formulated a new thin piezoelectric solid finite element in the form of shell and plate elements. When considering piezoelectrics in conjunction with structural members, linear piezoelectric theory simplifies the piezoelectric effect. Linear piezoelectric theory assumes an isothermal adiabatic process and quasi-static electric field equations. This research presents a comparison of the fully coupled electricalstructural finite element analysis of an isotropic panel with a surface mounted piezoelectric patch to experimental results. PIEZOELECTRIC RELATIONS Piezoelectric material inherently possesses coupling between electrostatics and structural dynamics. Linear piezoelectric theory yields an intrinsically coupled pair of piezoelectric constitutive equations. One describes the direct piezoelectric effect where the state of strain gives rise to an electric polarization, and the other describes the converse effect where an applied electrical field develops a state of strain. For a thin piezoelectric layer, the following constitutive relations result from linear piezoelectric theory (1)