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2 Mechanics and Mechanical Engineering

2 2018

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Transport of temperature fluctuations across a two-phased laminate conductor

Wodzyński Ł., Kula D., Wierzbicki E.

Mechanics and Mechanical Engineering

2018

Vol. 22, nr 3

775--787

In the periodic composite materials temperature or displacement fluctuations suppressed in directions perpendicular to the periodicity surfaces should expect a damping reaction from the composite. This phenomenon, known as the boundary effect behavior has been investigated only in the framework of approximated models. In this paper extended tolerance model of heat transfer in periodic composites is used as a tool allows analytical investigations of highly oscillating boundary thermal loadings. It has been shown that mentioned reaction is dual - different for even and odd fluctuations.

Fourier variant homogenization treatment of single impulse boundary effect behaviour

Kula D., Wierzbicki E., Witkowska-Dobrev J., Wodzyński Ł.

Mechanics and Mechanical Engineering

2018

Vol. 22, nr 3

683--690

Boundary effect behavior understood as near-boundary suppression of boundary fluctuation loads is described in various ways depending on the mathematical representation of solutions and the type of the center. In the case of periodic composites, the homogenization method is decisive here. In the framework of the Tolerance Averaging Approach, developed by prof. Cz. Wo´zniak leading to an approximate model of phenomena related to periodic composites this effect is described by a homogeneous part of differential equation for fluctuation amplitudes and usually this approximate description of the boundary effect behavior is restricted to a single fluctuation. In this paper, contrary to the previous elaborations, the boundary effect is developed in the variant of the tolerance thermal conductivity model in which the temperature field is represented by the Fourier expansions composed by an average temperature with infinite number of Fourier terms imposed on the average temperature as tolerance fluctuation suppressed in the framework of the boundary effect.