Free transverse vibration analysis of an elastically connected annular and circular double-membrane compound system

In this paper, free transversal vibrations of a systems of two annular and circular membranes connected by a Winkler elastic layer are studied using analytical methods and numerical simulation. At first the motion of each system is described by two homogeneous partial differential equations. The general solutions of the free vibrations are derived by the Bernoulli-Fourier method and the boundary problems are solved. The natural frequencies and natural mode shapes of vibrations of systems under consideration are determined. The investigation of free vibrations prove that the double-membrane systems execute two kinds of vibrations, synchronous and asynchronous. Then for each system two models formulated by using finite element representations are prepared. The FE models are manually tuned to reduce the difference between the natural frequencies of the analytical solutions and the natural frequencies of the FE model calculations, respectively.