EXACT ANALYSIS OF COUPLED ELECTROELASTIC BEHAVIOR OF A PIEZOELECTRIC PLATE UNDER CYLINDRICAL BENDING

An exact analysis of a piezoelectric plate under cylindrical bending is presented. The solutions for deformations, stresses, electric potential and electric displacement of a simply supported plate subjected to sinusoidal mechanical loading and electric potential on the top surface, electric potential alone at the bottom surface, and zero electric potential at the edges are derived. The numerical results of a specific case of the above formulation taking the potential zero at the top surface are presented. From study of these results it is recommended that a linear variation of deformations and of electric potential across thickness can safely be used for modelling the behaviour of a coupled piezoelectric plate under cylindrical bending when the length-to-thickness ratio is greater than about six, while higher-order modelling is required for thicker plates.