Dynamic response of functionally graded beams under moving heat source

As a first endeavor, the dynamic response of functionally graded (FG) beams under a moving heat source is investigated. The material properties are assumed to be temperature-dependent and graded in the thickness direction. A two-dimensional finite element method (FEM) is employed to obtain the temperature distribution throughout the beam. Then, the effect of a two-dimensional variation of temperature on the dynamic response of an FG beam with arbitrary boundary conditions is formulated based on the first-order shear deformation beam theory (FSDBT). The resulting equations of motion are transformed into a system of algebraic equation by employing the FEM in conjunction with Newmark's time integration scheme. In order to validate the formulation and method of solution, the exact solution is achieved in the case of isotropic beams with simply supported boundary conditions. It is shown that good agreement exists between the presented approach and the exact solution. Finally, the effect of different parameters on the dynamic response of FG beams under moving heat source is studied.