In the paper, the dynamic buckling of axially functionally graded beams under coupled stress wave propagating and dynamic buckling is investigated. The bucking governing equation and the boundary conditions at the compression stress wave front for a axially functionally graded beams are established based on the Infinitesimal section force balance condition and the principle of conservation of energy. A numerical method is introduced to transfer the varying coefficients differential equation into the linear algebraic equation sets, in which the displacement function expressed with Taylor/Chebyshev polynomials expansion. And then the eigen-equation for the axially functionally graded beams with non-uniform cross-section is obtained. Moreover, a numerical investigation for dynamic buckling of the axially functionally graded beams is carried out discussing the effects of variable cross-section and material inhomogeneity on critical buckling force parameters. The results shows that the present method has good accuracy and convergence.
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