Dynamic behaviors of tapered bi-directional functionally graded beams with various boundary conditions under action of a moving harmonic load

Abstract In this paper, the dynamic response of beams made of bi-directional functionally graded materials (FGMs) with varied cross-sections subjected to a moving harmonic load has been studied by a developed boundary-domain integral equation method based on the two-dimensional linear elastic theory. It is assumed that the elastic modulus and mass density of the FG beams vary separately following each exponential distribution parameters through longitudinal or transvers direction. Then, the elastostatic homogeneous fundamental solution was substituted into the dynamic governing equation for deriving the vibration boundary-domain integral equation of the tapered FG beams. A meshfree scheme can be achieved by applying the radial integration technique to transform the domain integrals into boundary integrals. Houbolt's algorithm is employed to obtain the dynamic response of the tapered FG beams. The effectiveness of the present method applied to the non-uniformed FG beams is verified by comparing numerical results with those available for free vibration of tapered beams of linearly variable width or depth. A detailed parametric study is carried out to investigate the influences of the taper ratios, material gradients, gradation directions and boundary conditions as well as the moving load frequencies and velocities on the dynamic behaviors of tapered FG beams.