International Applied Mechanics

, Volume 32, Issue 7, pp 524–531 | Cite as

Three-wave interaction and second harmonic generation in one-phase and two-phase hyperelastic media

  • Ya. Ya. Rushchitskii


We have applied the method of slowly varying amplitudes to the equations describing plane waves in one- phase and two-phase hyperelastic media. As a result, we have obtained the evolution equations for the complex amplitudes and Manley-Rowe power relations for both media. We have taken into account three-wave interaction and have established the spatial synchronization conditions (index matching conditions) for the triplet. We briefly analyze the second harmonic generation problem.


Evolution Equation Plane Wave Generation Problem Power Relation Harmonic Generation 
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  1. 1.
    Z. A. Gol'dberg, “Interaction of longinidinal and transverse plane waves.” Akust. Zh.,6, No. 2. 307–310 (1960).Google Scholar
  2. 2.
    L. K. Zarembo and V. A. Krasil'nikov, Introduction to Nonlinear Acoustics [in Russian] Nauka, Moscow (1966).Google Scholar
  3. 3.
    M. V. Kapranov, V. N. Kuleshov, and G. M. Utkin, Theory of Oscillations in Radio Engineering [in Russian], Nauka, Moscow (1984).Google Scholar
  4. 4.
    V. V. Krylov and V. A. Krasil'nikov, Introduction to Physical Acoustics [in Russian], Nauka, Moscow (1986).Google Scholar
  5. 5.
    Ya. Ya. Rushchitskii, “Interaction of elastic waves in two-phase material,” Prikl. Mekh.,28, No. 5, 13–22 (1992).Google Scholar
  6. 6.
    Ya. Ya. Rushchitskii, “Resonance interaction of nonlinear waves in two-phase mixtures,” Prikl. Mekh.,30, No. 5, 32–41 (1994).Google Scholar
  7. 7.
    A. P. Sukhorukov, Nonlinear Wave Interactions in Optics and Radiophysics [in Russian], Nauka, Moscow (1988).Google Scholar
  8. 8.
    M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981).Google Scholar
  9. 9.
    F. P. Bretherton, “Resonant interaction between waves. The case of discrete oscillations,” J. Fluid Mech.,20, No. 3, 457–479 (1964).Google Scholar
  10. 10.
    G. L. Jones and D. R. Kobett, “Interaction of elastic waves in an isotropic solid,” J. Acoust. Soc. Am.,35, No. 3, 5–10 (1963).Google Scholar
  11. 11.
    O. M. Phillips, “Wave interactions,” in: Nonlinear Waves, S. Leibowich and A. R. Seebass (eds.), Cornell University, New York-London (1974).Google Scholar
  12. 12.
    J. J. Rushchitsky, “Wave triplets in two-phase composites,” Mech. Composite Materials, No. 5, 660–670 (1995).Google Scholar
  13. 13.
    G. B. Whitham, Linear and Nonlinear Waves, Wiley Interscience, New York (1974).Google Scholar
  14. 14.
    A. Yariu, Quantum Electronics, Wiley, New York (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Ya. Ya. Rushchitskii
    • 1
  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKiev

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