Structural analogies on systems of deformable bodies coupled with non-linear layers

Abstract

The paper is addressed at phenomenological mapping and mathematical analogies of oscillatory regimes in systems of coupled deformable bodies. Systems consist of coupled deformable bodies like plates, beams, belts or membranes that are connected through visco-elastic non-linear layer, modeled by continuously distributed elements of Kelvin-Voigt type with nonlinearity of third order. Using the mathematical analogies the similarities of structural models in systems of plates, beams, belts or membranes are obvious. The structural models consist by a set of two coupled non-homogenous partial non-linear differential equations. The problems to solve are divided into space and time domains by the classical Bernoulli-Fourier method. In the time domains the systems of coupled ordinary non-linear differential equations are completely analog for different systems of deformable bodies and are solved by using the Krilov-Bogolyubov-Mitropolskiy asymptotic method. This paper presents the beauty of mathematical analytical calculus which could be the same even for physically different systems. The mathematical numerical calculus is a powerful and useful tool for making the final conclusions between many input and output values. The conclusions about nonlinear phenomena in multi-body systems dynamics have been revealed from the particular example of double plate's system stationary and non-stationary oscillatory regimes.