An efficient quadrilateral element for thermo-mechanical vibration characteristics of functionally graded plates with micro-structural defects

Abstract This work presents a finite element formulation for the vibration analysis of functionally graded material (FGM) plates containing microstructural defects operating in thermal environments. The material properties are assumed to be temperature-dependent and are modeled as higher-order functions of temperature. The volume fractions of the constituent materials are varied through the plate thickness according to a power-law distribution. The effective material properties of the FGM are evaluated using both the Mori–Tanaka homogenization scheme and the rule of mixtures. The kinematics of the FGM plates are described using an efficient layerwise theory. The governing equations of motion, constitutive relations, and boundary conditions are derived using on Hamilton’s principle. The stiffness coefficients of the plates are computed using a sub-laminate mechanics approach, wherein the plate thickness is discretized into several thin sublayers, each assumed to possess uniform material properties. This approach is particularly effective for micromechanical models where exact analytical integration of stiffness coefficients is difficult due to the complex polynomial variation of properties across the thickness. A four-noded quadrilateral finite element, previously developed for laminated and FGM shells, is extended in this study to analyze the dynamic behavior of FGM plates with microstructural defects and temperature dependent material properties. The natural frequencies are obtained using a subspace iteration technique, while the transient responses under step and impulse excitations are computed using the state-space form of the governing dynamic equations. The proposed finite element model is validated against three-dimensional elasticity and Ritz-based semi-analytical solutions, demonstrating excellent accuracy and reliability across varying thermal environments. A detailed parametric study is also carried out to investigate the effects of temperature, inhomogeneity index, porosity concentration, boundary conditions, and geometric parameters on the natural frequencies and transient responses of porous FGM plates.