Forced dynamic analysis of functionally graded beams under harmonic moving loads on elastic foundation with the finite element method

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Abstract
Introduction/purpose: This paper presents a numerical study of the forced dynamic behavior of a functionally graded beam subjected to a harmonically varying transversely concentrated moving force using a higher-order shear deformation theory. Methods: The governing equations are derived using Hamilton's principle. These equations are then transformed into the weak form using the Galerkin method. The problem is solved using the finite element method by developing a three-node finite element with four degrees of freedom per node. The Newmark beta method is chosen for the time integration and the Gauss method for the spatial integration. Results: The effects of several parameters were investigated, including the slenderness ratio, the material index, foundation stiffness, velocity and the frequency of the moving load. Good agreement was observed with the results obtained from the literature. Conclusion: This study illustrates the importance of using a higher order theory in the case of short beams and clearly shows the change in the behavior of the FGM beam as a function of different parameters.

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