On the Linear and Nonlinear Free Vibration of Functionally Graded Material Plates in the Thermal Environment

Abstract

Functionally graded material (FGM) is an advanced, microscopically homogeneous material, mainly composed of a mixture of metal and ceramic. The concept of FGM was first conceptualised in 1984 as a heat resistant material and since then used for special designing of high-temperature applications like aerospace, rocket heat shields, heat exchanger tubes, thermal barrier coating, nuclear reactor, etc. In FGM, the material properties undergo a gradual and smooth variation from one surface to another along a predetermined direction. The variation of volume fraction eliminates the interface problem by alleviating thermal stress concentration in high-thermal environment. A general nonlinear mathematical model for an FGM plate has been employed using the Green-Lagrange nonlinear kinematics in the framework of higher order shear deformation plate theory (HSDT). The material properties are considered temperature dependent to achieve an accurate analysis. The plate domain is discretised into eight noded isoparametric serendipity elements and employed Voigt-micromechanical model to ascertain the effective material properties of the constituents (ceramic, metal). A C0 continuity displacement field is derived from HSDT mid-plane kinematics to simplify the calculation and decrease the runtime in non-linear analysis. Sometimes, the vibration in structural components, lead to fatigue and failure of structural components, thereby results in performance reduction due to energy losses. Plate structures made of FGMs are subjected to different dynamic loading conditions during their service life and thereby, the structural linear and nonlinear vibration responses are affected considerably. To achieve the exact structural flexibility and the generality of the model, all the nonlinear higher-order strain terms are incorporated in the mathematical model. The governing equation of FGM plate structure is obtained using Hamilton’s variational principle and direct iteration technique is employed to obtain the desired nonlinear structural response in conjunction with finite element method. The convergence behaviour has been checked and the mathematical model is validated by comparing the obtained results with those of published literature. The vibration analysis has been carried out for FGM plates in thermal environment, skew FGM plates in thermal environment, FGM plates resting on elastic foundation in thermal environment, FGM plates in hygrothermal environment and rotating cantilever FGM plates in thermal environment, using linear and nonlinear
mathematical model. Finally, the effect of different geometrical and mechanical parameters, support conditions, temperature gradient on the linear and nonlinear frequencies are examined and discussed.