Dynamic response of bidirectional functionally graded beams with elastic supports and foundations under moving harmonic loads

Dynamic behavior of elastically supported bidirectional functionally graded (BDFG) beams resting on an elastic foundation under a moving harmonic load is investigated based on Chebyshev collocation method. Material properties of the BDFG beam are assumed to vary along the length and thickness of the beam according to a power-law function. The Hamilton’s principle is first used to derive the governing equations of motion of BDFG beams; then, the Chebyshev collocation method is applied to analyze the dynamic response. The backward differentiation formula method is employed to solve the transient ordinary differential equations to obtain the dynamic response of the beam. To assure the accuracy of the proposed model, some results are compared with those in the published literature. A good agreement is achieved between the two. Parametric studies are then carried out to explore the effects of slenderness ratios, thickness and length material graded indexes, excitation frequencies and speeds of moving loads, foundation stiffness coefficients and elastic support conditions on the dynamic characteristics of BDFG beams. It is believed that the presented model is valuable for the parametric studies and can better understand the various material, geometric and loading parameters affecting the dynamic response of the BDFG beam.