Vibrations of timoshenko beam‐columns on two‐parameter elastic foundations

A finite element procedure is developed for analysing the flexural vibrations of a uniform Timoshenko beam-column on a two-parameter elastic foundation. The beam-column is discretized into a number of simple elements with four degrees of freedom each. The governing matrix equation for small-amplitude, free vibrations of the beam-column on the elastic foundation is derived from Hamilton's principle. Several numerical examples are provided to show the effects of axial force, foundation stiffness parameters, partial elastic foundation, shear deformation and rotatory inertia on the natural frequencies of the beam-column.

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