New Element Formulation for Free Vibration Analysis of Timoshenko Beam on Pasternak Elastic Foundation

In this paper, the free vibration of the beam on elastic foundation is studied using finite element method. To this end, a two- node Timoshenko element is used for beam modeling. Each node in this element has a rotational and translational degree of freedom, which encompasses all four degrees of freedom. The displacement and rotational fields of this beam is selected from the third and the second order, respectively. Moreover, the shear strain of the element is assumed as a constant value. Interpolation functions for displacement field and beam rotation are explicitly calculated by employing total beam energy and it's stationary with respect to shear strain. Also, two-parameter elastic foundation model is used. In this method, the soil is modeled as a layer of Winkler springs with a shear layer on it. Next, by utilizing the interpolation functions, the stiffness matrices of beam and foundation, as well as their mass matrices are introduced; hence, the free vibration analysis on the elastic foundation is carried out. Finally, after conducting several tests, the high efficiency and accuracy of the proposed element is demonstrated.