Comparative analysis of the profile evolutions of an elastic harmonic wave caused by the second and third harmonics

International Applied Mechanics

Volumn 40, Issue 2, 2004, Pages 183-189

  Cattani, C ^a   Rushchitsky, J J ^b   Sinchilo, S V ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b S P TIMOSHENKO INSTITUTE OF MECHANICS   (Ukraine)

Author keywords

Composite materials; Computer simulation; New schemes of evolution; Nonlinear waves; Quadratically and cubically nonlinear waves

Indexed keywords

ELASTIC MEDIA; HARMONIC WAVE; NONLINEAR WAVES; RADIOPHYSICS;

APPROXIMATION THEORY; COMPOSITE MATERIALS; COMPUTER SIMULATION; DEFORMATION; HARMONIC ANALYSIS; HYDRODYNAMICS; NONLINEAR EQUATIONS; OSCILLATIONS; POLARIZATION;

WAVE PROPAGATION;

EID: 3543144958     PISSN: 10637095     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:INAM.0000028597.32722.be     Document Type: Review

References (23)

1. M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhomkov, Theory of Waves [in Russian], Nauka, Moscow (1990).
2. V. I. Erofeev, Wave Processes in Rigid Bodies with Microstructure [in Russian], Izd. Mosk. Univ., Moscow (1999).
3. L. K. Zarembo and V. A. Krasil'nikov, An Introduction to Nonlinear Acoustics [in Russian], Nauka, Moscow (1966).
4. V. V. Krylov and V. A. Krasil'nikov, An Introduction to Physical Acoustics [in Russian], Nauka, Moscow, (1986).
5. M. I. Rabinovich and D. I. Trubetskov, An Introduction to the Theory of Vibrations and Waves [in Russian], Nauka, Moscow (1984).
6. J. J. Rushchitsky and S. I. Tsurpal, Waves in Microstructural Materials [in Ukrainian], Inst. Mekh. im. S. P. Timoshenko, Kiev (1998).
7. A. P. Sukhomkov, Nonlinear Wave Interactions in Optics and Radiophysics [in Russian], Nauka, Moscow (1988).
8. L. Ascione and A. Grimaldi, Elementi di Meccanica del Continua, Massimo, Napoli (1993).
9. C. Banfi, Introduzione alla Meccanica dei Continui, CEDAM, Padova (1990).
10. C. Cattani and J. J. Rushchitsky, "Nonlinear acoustic waves in materials: retrospect and some new lines of development," in: Abstracts of Papers Read at Int. Workshop on Potential Flows and Complex Analysis, September, Kiev, Ukraine (2002), pp. 11-12.
11. C. Cattani and J. J. Rushchitsky, "Plane waves in cubically nonlinear elastic waves," Int. Appl. Mech., 38, No. 11, 1361-1365 (2002).
12. C. Cattani, J. J. Rushchitsky, and S. V. Sinchilo, "Propagation of the energy of nonlinearly elastic plane waves," Int. Appl. Mech., 39, No. 5, 583-586 (2003).
13. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin (1999).
14. W. Nowacki, Teoria Sprezystosci, PWN, Warsaw (1970).
15. J. J. Rushchitsky, "Extension of the microstructural theory of two-phase mixtures to composite materials," Int. Appl. Mech., 36, No. 5, 586-614 (2000).
16. J. J. Rushchitsky. "Interaction of waves in solid mixtures," Appl. Mech. Rev., 52, No. 2, 34-74 (1999).
17. J. J. Rushchitsky and C. Cattani, "Generation of the third harmonics by plane waves in Murnaghan materials.," Int. Appl. Mech., 38, No. 12, 1482-1487 (2002).
18. J. J. Rushchitsky, I. M. Khotenko, and K. V. Savelieva, "The third harmonics generation by plane shear waves in a piezopowder," in: Annotations of the 20th Symp. on Vibrations in Physical Systems, Poznan, Poland (2002), pp. 256-257.
19. J. J. Rushchitsky, I. M. Khotenko, and K. V. Savelieva, "Plane shear waves in piezopowders: unexpected new phenomenon-the third harmonics generation," in: Books of Abstracts of the 30th Int. Summer School Advanced Problems in Mechanics, St. Petersburg, Russia (2002), p. 84.
20. J. J. Rushchitsky, K. V. Savel'eva, and A. P. Kovalenko, "Self-generation of transverse waves in hyperelastic media (the third approximation)," Int. Appl. Mech., 32, No. 6, 536-544 (1996).
21. Y. R. Shen, The Principles of Nonlinear Optics, John Wiley, New York (1984).
22. M. Schubert and B.Wilgelmi, Einfuhrung in die nichtlineare Optik, Teil l. Klassische Beschreibung, BSB B.G. Teubner Verlagsgesellschaft, Leipzig (1971).
23. A. Yariv, Quantuni Electronics, John Wiley, New York (1967).