Free vibration and buckling analysis of functionally graded deep beam-columns on two-parameter elastic foundations using the differential quadrature method

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Abstract
In this research, a differential quadrature method is applied for free vibration and buckling analysis of deep beam-columns composed of functionally graded materials on two-parameter elastic foundations. Derivation of equations is based on the unconstrained higher-order shear deformation theory taking into account the complete effects of shear deformation, depth change, and rotary inertia. It is assumed that the effective mechanical properties of functionally graded (FG) beam-columns are temperature dependent and vary continuously throughout the thickness direction according to volume fraction of the constituents defined by power-law function. The accuracy, convergence, and flexibility of the differential quadrature technique for simply supported FG deep beam-columns with complicated governing differential equations and boundary conditions are examined and verified with the known data in the literature.

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