Application of Chebyshev collocation element method to Green-Naghdi thermoelasticity of a bi-layered media consists of FGM and viscoelastic domains

Abstract

In this study, the generalized coupled thermoelastic wave propagation and temporal evolution in a bi-layered system are analyzed. The main layer is made of functionally graded materials (FGM), while the holder layer is viscoelastic. The constituent volume fractions in the FGM layer are calculated by a power law function. Moreover, the Voigt rule of mixtures is employed to obtain the homogenized material properties. On the other hand, the constitutive law for the viscoelastic environment is considered based on the Kelvin-Voigt model. The heat conduction equation for each layer is represented based on the general form of the Green-Naghdi theory. First, for each layer, two motion and heat conduction coupled equations are derived, as well as the boundary and appropriate continuity conditions. The Chebyshev collocation element (CCE) method is used to solve the spatial-dependent parts of equations and also assemble the governing matrices into a global system. Finally, the Newmark numerical integration method is implemented to solve the ODEs and calculate the system response. The achieved response is verified with limited articles in the literature. Some parametric results are shown to evaluate the performance of FG and viscoelastic characteristics on the FGM layer response which is subjected to a thermal shock.