Free vibration of the Timoshenko beam interacting with the Winkler foundation

In the study a free transverse vibration analysis of the simply supported Timoshenko beam on an arbitrary variable Winkler foundation is presented. The analysis is based on the use of the analytical method compared with numerical simulation. The elastic foundation is composed of two arbitrary variable, massless, regions of the Winkler type. At first the general solution of free vibration is derived by the separation of variable method. The natural frequencies of the system under consideration are determined. Then the models of the system formulated by using finite element technique are prepared and eigenvalue problem is solved. Achieved results of calculation are discussed and compared for these models. All needed finite element models are formulated by using ANSYS FE code. It is important to note that the data presented in the article is yielded the practical advice to design engineers.