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1 Journal of Technical Physics

1 2004

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Simplified models for the vibration analysis of micro-periodic elastic media

Rychlewska J., Szymczyk J., Woźniak C.

Journal of Technical Physics

2004

Vol. 45, no 2

91-104

The aim of this paper is to propose and apply a new approach to the formation of simplified models for the vibration analysis of a micro-periodic linear-elastic composite medium. First, we propose a discrete model which can be used to investigations of both long and short waves. The main feature of the obtained discrete model is the finite-difference form of governing equations. The continuum models are derived directly from the discrete one under the assumption that the macroscopic wavelength is large when compared to the length dimension of a periodicity cell. The proposed models describe both the low-frequency and high-frequency vibration problems and can be formulated on different levels of accuracy. The reliability of the procedure leading from discrete to continuum models is discussed on the illustrative example.