Thermoelastic vibration analysis of functionally graded skew plate using nonlinear finite element method

ABSTRACT

Numerical investigation of nonlinear free vibration of functionally graded skew (FGS) plate in the thermal environment is presented. The mathematical model is proposed for the first time based on higher order shear deformation theory in conjunction with Green–Lagrange-type geometric nonlinearity for the FGS plate subjected to a thermal load. The material properties are considered to be temperature dependent and are graded along the thickness direction as per simple power law of distribution in terms of volume fraction of the constituent phase. The governing algebraic equations are derived using Hamilton’s principle, and the solutions are obtained using the direct iterative method. The proposed finite element model has discretized into an eight-noded quadratic serendipity elements. To validate the model, the obtained results are compared with the available literature. The influence of volume fraction index, skew angle, temperature change, aspect ratio, side–thickness ratio, and boundary conditions on the linear and nonlinear frequency of skew functionally graded material plate is examined and discussed in detail.

KEYWORDS:

• Direct iterative method
• functionally graded material
• Green–Lagrange nonlinearity
• HODT
• nonlinear finite element model
• simple power law
• skew angle