Nonlinear dynamic responses of functionally graded tubes subjected to moving load based on a refined beam model

Abstract

In the paper, basing on a refined beam model and considering the effects of thermal and elastic foundation, the nonlinear dynamic responses of functionally graded tubes applied to a moving load which keeps at a constant velocity are studied. This refined beam model is expanded by Laurent series expansion which can fulfill the shear stress on the inner and outer surfaces. The whole governing equations are obtained by Hamilton’s principle, and solved by Galerkin method and Newmark method. In the numerical examples, the effects of transverse shear deformation, geometric nonlinearity, functionally graded index, inner radius, temperature, elastic foundation stiffness, and velocity of moving load on the dynamic responses of FGM tubes are discussed. For present beam model, it is more suitable and convenient to analyze the nonlinear dynamic responses of FGM tubes with circular cross section subjected to a moving load, especially for exact stress analysis.