Plane waves in nano-composite materials

Authors

  • K. V. Savelieva S. P. Timoshenko Institute of Mechanics NAS of Ukraine, 03057, Kyiv, P. Nesterov str., 3
  • O. G. Dashko S. P. Timoshenko Institute of Mechanics NAS of Ukraine, 03057, Kyiv, P. Nesterov str., 3
  • Y. V. Simchuk National Technical University of Ukraine “I. Sikorsky Kyiv Polytechnic Institute”, 03056, Kyiv, Peremoghy pr., 37

DOI:

https://doi.org/10.17721/1812-5409.2019/1.46

Abstract

The propagation of plane waves in a hyper-elastic medium is theoretically investigated. Two methods of research were used: the method of slowly variable amplitudes and the method of perturbations (successive approximations). The results obtained by these methods are analyzed. The wave interaction in nanocomposite materials is studied. A theoretical study of the cubically nonlinear elastic interaction of plane harmonic waves is carried out for a material whose nonlinear properties are described by the Murnaghan elastic potential. The solution for self-generation of the longitudinal wave is obtained by the method of slowly varying amplitudes. The interaction of transverse horizontally and vertically polarized harmonic waves are studied using the perturbing method. The pumping of energy between different harmonics of a longitudinal wave and various types of transverse waves is described analytically. The results of numerical analysis for various types of nanocomposite materials are presented.

Key words: cubic nonlinearity, elastic plane wave, nanocomposite materials, method of slowly varying amplitudes, perturbation method.

Pages of the article in the issue: 198-201

Language of the article: Ukrainian

References

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How to Cite

Savelieva, K. V., Dashko, O. G., & Simchuk, Y. V. (2019). Plane waves in nano-composite materials. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (1), 198–201. https://doi.org/10.17721/1812-5409.2019/1.46

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Section

Differential equations, mathematical physics and mechanics