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The Subharmonic Resonance and Second Harmonic of a Plane Wave in Nonlinearly Elastic Bodies

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Abstract

Similarities of the subharmonic resonance in linear mechanical systems and of the second harmonic of a plane wave in nonlinearly deformable elastic bodies are described

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REFERENCES

  1. A. A. Andronov, A. A. Vitt, and S. É. Khaikin, Theory of Oscillations [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  2. L. K. Zarembo and V. A. Krasil'nikov, An Introduction to Nonlinear Acoustics [in Ukrainian], Nauka, Moscow (1966).

    Google Scholar 

  3. V. V. Migulin, V. I. Medvedev, E. R. Mustel', and V. N. Parygin, Fundamentals of Vibration Theory[in Russian], Nauka, Moscow (1978).

    Google Scholar 

  4. Ya. Ya. Rushchitskii and S. I. Tsurpal, Waves in Materials with a Microstructure [in Russian], Inst. Mekh. NAN Ukrainy, Kiev (1998).

    Google Scholar 

  5. Ya. Ya. Rushchitskii and B. B. Érgashev, “Some features of the natural vibrations of a mixture,” Prikl. Mekh., 26, No. 1, 16–22 (1990).

    Google Scholar 

  6. S. P. Strelkov, An Introduction to Vibration Theory [in Russian], Nauka, Moscow (1964).

    Google Scholar 

  7. C. Cattani and Ya. Ya. Rushchitskii, “Plane waves in cubically nonlinear elastic media,” Int. Appl. Mech., 38, No. 11, 1361–1365 (2002).

    Google Scholar 

  8. K. Magnus, Eine Einführung in die theoretische Behandlung von Schwingungsproblemen, B. G. Teubner, Stuttgart (1976).

  9. J. J. Rushchitsky, “Interaction of waves in solid mixtures,” Appl. Mech. Rev., 52, No. 2, 35–74 (1999).

    Google Scholar 

  10. Ya. Ya. Rushchitskii, “Extension of the microstructural theory of two-phase mixtures to composite materials,” Int. Appl. Mech., 36, No. 5, 586–614 (2000).

    Google Scholar 

  11. Y. Ya. Rushchitskii, “New solitary waves in elastic materials: existence and nonlinear interaction,” Int. Appl. Mech., 37, No. 7, 921–928 (2001).

    Google Scholar 

  12. Ya. Ya. Rushchitskii, “Self-switching of waves in materials,”Int. Appl. Mech., 37, No. 11, 1492–1498 (2001).

    Google Scholar 

  13. Ya. Ya. Rushchitskii and C. Cattani, “Generation of the third harmonics by plane waves in Murnaghan materials,” Int. Appl. Mech., 38, No. 12, 1482–1487 (2002).

    Google Scholar 

  14. G. Schmidt, Parametererregte Schwingungen, DVW, Berlin (1975).

    Google Scholar 

  15. Y. R. Shen, The Principles of Nonlinear Optics, John Willey and Sons, New York (1984).

    Google Scholar 

  16. G. B. Whitham, Linear and Nonlinear Waves, John Willey and Sons, New York (1974).

    Google Scholar 

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Cattani, C., Rushchitskii, Y.Y. The Subharmonic Resonance and Second Harmonic of a Plane Wave in Nonlinearly Elastic Bodies. International Applied Mechanics 39, 93–98 (2003). https://doi.org/10.1023/A:1023624318599

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  • DOI: https://doi.org/10.1023/A:1023624318599

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