In this study the in plane flexural vibration of a system of circular ring interacting with elastic foundation is presented on the basis of the analytical method and numerical simulation. The elastic foundation is described by the Winkler model. At first the motion of the system is described by partial differential equations. The effect of rotary inertia and shear deformation is included. The general solution of the free vibration is derived by the separation of variable method and the boundary problem is solved. The second model is formulated by using finite element representations. The natural frequencies and natural mode shapes of vibration of the system are determined. The obtained results of calculation are discussed and compared for these two models. FE models are formulated by using ANSYS code. It is important to note that the data presented in the paper brings practical advice to design engineers.
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