Vibration response analysis of the bi-directional porous functionally graded piezoelectric (BD-FGP) plate

The current paper investigates the free vibration characteristics of the bidirectional functionally graded piezoelectric (BD-FGP) porous plate subjected to thermal and electrical loading. The properties of the plate vary as power-law distributions in two directions, that is, longitudinal and transverse directions. The BD-FGP plate is considered to be porous of two types even type and uneven type. The governing equation of the BD-FGP plate is attained with the Von Karman nonlinear strains associated with the FSDT displacement field and Hamilton's principle. Also, the 9-noded Lagrange quadrilateral element with seven degrees of freedom (DOFS) discretized the BD-FGP plate and solved it by the higher-order finite element (HOFE) method. The present formulation's convergence and accuracy are confirmed by comparing the attained results with the literature. The influence of the various parameters includes thickness ratios, porous exponent, volume fraction exponent, electrical loading, thermal loading, and support conditions. The investigations of the current study show that the material variations in both directions, that is, longitudinal and transverse, have significant importance in the design and development of modern smart structures and their components of engineering applications.