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Thermodynamic analogy in problems of high-frequency vibration propagation in complex systems

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Abstract

A theoretical description taking into account the inhomogeneity of complex systems and the insufficiency of statistical information about the geometric properties and mechanical parameters of materials in the framework of a unified approach is proposed. The unification is based on representing the system as an enormous number of substructures with unreliable mechanical and geometric parameters. In the case where the density of natural frequencies of substructures is rather high, analytical expressions are obtained for the mean energy of a substructure and for its spherical density. Similar formulas are derived for the spectral densities of the applied, scattered, and transferred powers of vibration flows. The equations describing the high-frequency vibration energy transfer between substructures are obtained. It is shown that the vibration energy flow in complex systems and its redistribution between substructures obeys the equation which is a mechanical analog of the discrete form of the generalized Fourier law in heat conduction theory.

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Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol’shoy pr. 61, St. Petersburg, 199178, Russia

    A. K. Belyaev

Authors
  1. A. K. Belyaev
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Correspondence to A. K. Belyaev.

Additional information

Original Russian Text © A.K. Belyaev, 2015, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2015, No. 2, pp. 129–138.

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Belyaev, A.K. Thermodynamic analogy in problems of high-frequency vibration propagation in complex systems. Mech. Solids 50, 218–226 (2015). https://doi.org/10.3103/S0025654415020119

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  • DOI: https://doi.org/10.3103/S0025654415020119

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