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IssuesArchive of Issues2015-2pp.218-226

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A.K. Belyaev, "Thermodynamic Analogy in Problems of High-Frequency Vibration Propagation in Complex Systems," Mech. Solids. 50 (2), 218-226 (2015)
Year 2015 Volume 50 Number 2 Pages 218-226
DOI 10.3103/S0025654415020119
Title Thermodynamic Analogy in Problems of High-Frequency Vibration Propagation in Complex Systems
Author(s) A.K. Belyaev (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr. 61, St. Petersburg, 199178 Russia, vice.ipme@gmail.ru)
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.
Keywords high-frequency vibration, microplasticity, random parameters, vibration energy, generalized Fourier law
References
1.  E. V. Lomakin, "Constitutive Models of Mechanical Behavior of Media with Stress State Dependent Material Properties," in Series: Advanced Structural Materials, Vol. 7. Mechanics of Generalized Continua (Springer, Berlin, 2011), pp. 339-350.
2.  E. V. Lomakin and B. N. Fedulov, "Theory of Plasticity and Limit Equilibrium of Bodies Sensitive to Stress State Type," Vestnik NNGU, No. 4, 1585-1587 (2011).
3.  V. A. Palmov, Vibrations of Elastoplastic Bodies (Nauka, Moscow, 1976) [in Russian].
4.  A. I. Lurie, Analytic Mechanics (Fizmatgiz, Moscow, 1961) [in Russian].
5.  V. V. Bolotin, Random Vibrations of Elastic Systems (Nauka, Moscow, 1979) [in Russian].
6.  A. K. Belyaev and V. A. Palmov, "Integral Theories of Random Vibrations of Complex Structures," in Random Vibration - Status and Recent Developments, Ed. by I. Elishakoff and R. H. Lyon (Elsevier, Amsterdam, 1986), pp. 19-38.
Received 06 October 2014
Link to Fulltext http://link.springer.com/article/10.3103/S0025654415020119
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