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1 Vibrations in Physical Systems

1 2012

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Microlocal modelling in elastodynamic of periodically compound plates

Jeleniewicz K., Nagórko W.

Vibrations in Physical Systems

2012

Vol. 25

185--192

In the paper, we will present certain method of modelling of elastic, heterogeneous, anisotropic and periodically multicomponent plates. The method is called the microlocal homogenization or the homogenization with microlocal parameters. It differs from the currently known methods in the fact that it does not consist in solving the problem on the basic cell. The system of assumptions and set of modeling relationships is different from that in the classical method of asymptotic homogenization. There occur not only displacement and stress fields in a body, but also some new fields – microlocal parameters − that describe the behavior of a plate inside the basic cell. In the constructed model, there is 1 + n coupled equations, corresponding to three displacements and n microlocal parameters. Moreover, the model equations depend on some postulated functions called shape functions, which must be known. In the paper, we will propose such functions and carry out an analysis of free vibrations of multicomponent plates.