Natural frequencies are important dynamic characteristics of a structure where they are required for the forced vibration analysis and solution of resonant response. Therefore, the exact solution to free vibration of elastically restrained Timoshenko beam on an arbitrary variable elastic foundation using Green Function is presented in this paper. An accurate and direct modeling technique is introduced for modeling uniform Timoshenko beam with arbitrary boundary conditions. The applied method is based on the Green Function. Thus, the effect of the translational along with rotational support flexibilities, as well as, the elastic coefficient of Winkler foundation and other parameters are assessed. Finally, some numerical examples are shown to present the efficiency and simplicity of the Green Function in the new formulation.
In this article, the dynamic response of a non-uniform Timoshenko beam acted upon by a moving mass is extensively investigated. To this end, the eigenfunction expansion method is adapted to the problem, employing the natural mode shapes of a uniform Timoshenko beam. Moreover, the orthonormal polynomial series expansion method is successfully applied to the coupled set of governing differential equations pertaining to the dynamic behavior of non-uniform Timoshenko beam actuated by a moving mass. Some numerical examples are solved in which the excellent agreement of the two presented methods is illustrated.
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