The paper describes how to analytically solve hyperbolic system of partial differential equations describing the boundary effect phenomenon, obtained in the framework of the refined tolerance model of heat conduction in periodic composites [Kula and Wierzbicki 2015]. Basic unknowns of this model are coefficients of Fourier expansion representing the temperature field which represents an alternative exact description of the heat transfer in composite rigid conductors. The aim of this paper is to indicate two sinusoidal-type boundary impulses which cannot be transported independently by the two-phased periodic laminated composite. Investigation of the form of the suppression of thermal boundary fluctuations is important to allow the construction to minimize the destruction of composites caused by the rotations of fluctuation amplitudes which are transported by composite not independently.

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