Low‐Velocity Impact Response Analysis of Functionally Graded Piezoelectric Plates Using Finite‐Element Method and a Two‐Degrees‐of‐Freedom Spring‐Mass Model

Abstract

The study focuses on the low‐velocity impact response of functionally graded piezoelectric plates. The effective material properties are determined using the rule of mixture and power law model. The kinematics of the plates is modeled by the first‐order shear deformation theory, and coupled governing equations of the plates are formulated using Hamilton's principle and Maxwell's law. A set of time‐dependent equations, extracted by applying the finite‐element method, is solved by the fourth‐order Runge–Kutta method. A linearized form of Hertz's contact law and a two‐degrees‐of‐freedom spring‐mass system are incorporated to find the contact force under the impact event. Numerical results are verified by comparing with the available literature data. The impact response of the plates constituted of different volume fractions and slenderness ratios in both simply supported and clamped boundary conditions are evaluated under different impact conditions. Based on the results of the present study, it is found that the volume fraction of the piezoelectric components, impact condition, in‐plane dimensions, and the plate slenderness ratio play significant roles in the impact behavior of the plates. Eventually, it is found that the applied electric voltage is not a notable factor in determining the impact response of the plates.