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This study presents a static analysis and natural frequency analysis of functionally graded laminated piezoelectric beams based on the Euler–Bernoulli theory using the finite element method. A simple power law is used to vary all material properties across the thickness, except for Poisson’s ratio. The effect of laminate configuration and volume fraction index on the deflection and natural frequency of beams made of functionally graded piezoelectric materials (FGPM) is investigated, and the relationship between deflection and different volume fraction indices under thermal, electrical, and mechanical loads is explored. The study shows that there is a certain volume fraction index that maximizes or minimizes deflection. Additionally, the variation of natural frequency in relation to the power law index is examined. The findings of this research are useful for the development of sensors and actuators in different environments, and the appropriate operation point of the structure can be selected based on the behavior of the sensor or actuator of the beam.

This paper investigates the dynamic response of functionally graded piezoelectric plates using the finite element method based on first-order shear deformation theory. The plates are composed of materials with properties that vary across their thickness, following a simple power-law relationship with the volume fraction of the constituents. Different boundary conditions and configurations, such as FG plates with piezoelectric layers and FGP plates with piezoelectric layers, are considered to analyze the dynamic behavior of functionally graded piezoelectric material (FGPM) plates under mechanical and electrical loadings. Comparisons with previous studies validate the accuracy of the obtained results. Furthermore, the effects of various parameters, such as the power-law index, maximum displacement from static analysis, maximum displacement in the first vibration mode, and others, on the dynamic response of FGM and FGPM plates with piezoelectric layers are investigated. The results demonstrate the influence of different power-law exponents and piezoelectric layers on plate behavior. The findings show that the maximum static and dynamic deflections of the plate vary with the power-law index, but their ratio remains constant for all values of “n”. Additionally, the effect of electrical loading on the dynamic response of FGP plates is examined. The study reveals that the maximum dynamic displacement of the plates increases with the power-law constant under electrical loading. Overall, this study provides valuable insights into the dynamic response of functionally graded piezoelectric plates, contributing to the understanding and design of such structures in various engineering applications subjected to dynamic loading.