One-dimensional nonlinear vibration analysis and coupled thermoelasticity based on Green-Naghdi model

Abstract

The present article reports on a study on nonlinear coupled thermoelasticity based on Green-Naghdi type III model in one-dimensional form. Unlike other research in which temperature change is low and the strain relations are linear, in the present study the nonlinear finite strain assumption is governed. Two coupled nonlinear partial differential equations, namely; energy and linear momentum are established. The basic equations are formulated in material coordinates and then transformed into dimensionless form. The homotopy analysis method is used to analyze the one-dimensional structure. Two different cases are studied. The thermo-mechanical wave propagation with reflection from the boundary, and the influence of the damping parameter–presented in Green-Naghdi type III model–on temperature. The linear and nonlinear equations are compared. It should be noted that the nonlinear finite strain theory governs better when the loading temperature is high.