Vibration Analysis of Functionally Graded Piezoelectric Annular Sectorial Plates

Piezoelectric materials are one of the most common materials currently being studied for smart structures. But layered piezoelectric elements are easy to crack at interfaces. In order to overcome the interfacial stress concentrations of traditional piezoelectric elements, functionally graded piezoelectric materials with material properties varying smoothly and continuously along one (or more) directions) have been developed. In the design of functionally graded piezoelectric devices, the electromechanical coupled dynamic behavior is of great importance. A lot of research papers dealt with the dynamical responses of functionally graded piezoelectric materials components having regular geometric shape such as rectangle or circle. However, in many cases, the actual components have special shapes such as sector, annular sector, and ellipse and so on. Dynamical analysis of functionally graded piezoelectric materials irregular plates is also necessary. But, to the authors’ knowledge, researches on the vibration of functionally graded piezoelectric annular sectorial plates have not been seen until now. In the present work, the free and forced vibration characteristics of functionally graded piezoelectric annular sectorial plates with simply supported radial edges and arbitrary circular edges are studied. According to the three-dimensional elastic theory of piezoelectric materials and assuming that the mechanical and electric properties of the materials vary continuously along the thickness direction and have the same exponential distribution, the free and forced vibration analysis of functionally graded piezoelectric annular sectorial plates is achieved using the semi-analytical method which makes use of the state space method along the graded direction and the one-dimensional differential quadrature method along the radial direction. The accuracy and convergence of the present method are demonstrated through numerical results. Compared with finite element method, the semi-analytical method has great superiority in the vibration analysis of functionally graded piezoelectric annular sectorial plates. A detailed parametric study is carried out to show the effects of thickness ratios, radii ratios, sector angles, material property graded indexes, circumferential wave numbers, forcing frequencies and circumferential boundary conditions on the natural frequencies and dynamical responses of functionally graded piezoelectric annular sectorial plates. The method presented in this paper can be used in the coupling electromechanical analysis of functionally graded piezoelectric plates.