An isogeometric Bézier finite element method for vibration analysis of functionally graded piezoelectric material porous plates

Abstract

This work presents an isogeometric Bézier finite element method combined with a C0-type higher-order shear deformation theory for vibration analysis of functionally graded piezoelectric material porous (FGPMP) plates. The FGPMP plate made of a mixture of PZT-4 and PZT-5A/PZT-5H materials is considered in both perfect and imperfect forms. Material properties of FGPMP plates vary continuously through the thickness direction and are computed by a modified power-law formula. Two porosity models including even and uneven distributions are employed. To satisfy the Maxwell's equation in the quasi-static approximation, an electric potential field in the form of a mixture of a cosine and linear variation is adopted. The advantages of present approach are inherited all properties of the conventional finite element method (FEM) and the exact geometry of isogeometric analysis (IGA). The influence of external electric voltages, power-law index, porosity coefficient, porosity distribution; geometrical parameters, aspect ratios, and various boundary conditions on behaviors of structures is studied. Obtained results are compared with the analytical solution as well as those of several available numerical approaches. In addition, several FGPMP plates with curved geometries are studied furthermore. Although these geometries have not had any analytical solutions, they could be considered as reference solutions for future works.