Vibration of Timoshenko beams on three-parameter elastic foundation

In the present paper, the process of the formulation of the equations of dynamic equilibrium and of the respective equations of natural vibration of Timoshenko beams on three-parameter elastic foundation within the framework of the second order theory is presented. The corresponding mass matrices are also formulated. In order to define the values of the parameters of the three-parameter model, an analytical method is applied. With the aid of two numerical examples, it is proved that the three-parameter model is capable of yielding natural period values that sufficiently approximate those derived by the solution using 2D finite element soil models.