Numerical analysis of strongly nonlinear extensional vibrations in elastic rods

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

Volumn 54, Issue 1, 2007, Pages 96-106

  Vanhille, Christian ^a   Campos Pozuelo, Cleofé ^b  

^a UNIVERSIDAD REY JUAN CARLOS   (Spain)

^b Consejo Superior de Investigaciones Científicas   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DIFFERENTIAL EQUATIONS; ELASTICITY; NONDESTRUCTIVE EXAMINATION; NUMERICAL METHODS; ULTRASONICS;

ACOUSTIC CHARACTERIZATION; ELASTIC RODS; VIBRATION WAVEFORMS;

VIBRATIONS (MECHANICAL);

ACOUSTICS; ARTICLE; COMPUTER SIMULATION; ELASTICITY; MATERIALS; MECHANICAL STRESS; MOTION; NONLINEAR SYSTEM; RADIATION SCATTERING; THEORETICAL MODEL; VIBRATION;

ACOUSTICS; COMPUTER SIMULATION; ELASTICITY; MANUFACTURED MATERIALS; MODELS, THEORETICAL; MOTION; NONLINEAR DYNAMICS; SCATTERING, RADIATION; STRESS, MECHANICAL; VIBRATION;

EID: 33846277562     PISSN: 08853010     EISSN: None     Source Type: Journal    
DOI: 10.1109/TUFFC.2007.215     Document Type: Article

References (35)

1. J. A. Gallego-Juárez, G. Rodríguez-Coral, E. Riera-Franco de Sarabia, F. Vázquez-Martínez, C. Campos-Pozuelo, and V. M. Acosta-Aparicio, "Recent development in vibrating-plate macrosonic transducers," Ultrasonics, vol. 40, pp. 889-893, May 2002.
2. J. A. Gallego-Juárez, G. Rodríguez-Coral, E. Riera-Franco de Sarabia, F. Vázquez-Martínez, V. Acosta-Aparicio, and C. Campos-Pozuelo, "Development of industrial models of high-power stepped-plate sonic and ultrasonic transducers for use in fluids," in Proc. World Congress Ultrasonics/IEEE Int. Ultrason. Symp., 2001, pp. 571-578.
3. C. Campos-Pozuelo and J. A. Gallego-Juárez, "Limiting strain subjected to high-intensity ultrasound," Acta Acustica/Acustica, vol. 82, pp. 823-828, Nov. 1996.
4. C. Campos-Pozuelo, C. Vanhille, and J. A. Gallego-Juárez, "Comparative study of the nonlinear behaviour of fatigued and intact samples of metallic alloys," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 53, pp. 175-184, Jan. 2006.
5. K. Van Den Abeele, A. Sutin, J. Carmeliet, and P. A. Johnson, "Micro-damage diagnostics using nonlinear elastic wave spectroscopy (NEWS)," NDT&E Int., vol. 34, pp. 239-248, June 2001.
6. K. Van Den Abeele and J. Visscher, "Damage assessment in reinforced concrete using spectral and temporal nonlinear vibration techniques," Cement Concrete Res., vol. 30, pp. 1453-1464, Sep. 2000.
7. V. V. Kazakov and A. M. Sutin, "Pulsed sounding of cracks with the use of the modulation of ultrasound by vibrations," Acoust. Phys., vol. 47, pp. 308-312, 2001.
8. R. N. Thurston, "Wave propagation in fluids and normal solids," in Physical Acoustics. vol. I, pt. A, W. P. Mason, Ed. New York: Academic, 1964, pp. 1-110.
9. A. N. Noris, "Finite-amplitude waves in solids," in Nonlinear Acoustics. M. F. Hamilton and D. T. Blackstock, Eds. New York: Academic, 1998, pp. 263-277.
10. K. W. Winkler and X. Liu, "Measurements of third-order elastic constants in rocks," J. Acoust. Soc. Amer., vol. 100, pp. 1392-1398, Sep. 1996.
11. D. M. Egle and D. E. Bray, "Measurement of acoustoelastic and third-order elastic constants for rail steel," J. Acoust. Soc. Amer., vol. 60, no. 3, pp. 741-744, Sep. 1976.
12. S. Takahashi and R. Motegi, "Stress dependency on ultrasonic wave propagation velocity. Part 2: Third order elastic constants of steels," J. Mater. Sci., vol. 22, pp. 1857-1863, May 1987.
13. M. A. Breazeale and J. Philip, "Determination of third-order elastic constants from ultrasonic harmonic generation measurements," in Physical Acoustics, vol. XVII, W. P. Mason and R. N. Thurston, Eds. New York: Academic, 1984, pp. 1-60.
14. J. K. Na and M. A. Breazeale, "Ultrasonic nonlinear properties of lead zirconate titanate ceramics," J. Acoust. Soc. Amer., vol. 95, pp. 3213-3221, June 1994.
15. M. A. Breazeale, Comparison of the Nonlinear Behavior of Fluids and Solids. H. Hobaek, Ed. Singapore: World Scientific, 1993.
16. F. D. Murnaghan, Finite Deformation of an Elastic Solid. New York: Dover, 1951.
17. X. Gong, D. Zhang, J. Liu, H. Wang, Y. Yan, and X. Xu, "Study of acoustic nonlinearity parameter imaging methods in reflection mode for biological tissues," J. Acoust. Soc. Amer., vol. 116, pp. 1819-1825, Sep. 2004.
18. W. H. Jiang and W. W. Cao, "Nonlinear properties of lead zirconate-titanate piezoceramics," J. Appl. Phys., vol. 88, pp. 6684-6689, Dec. 2000.
19. R. M. D'Angelo, K. W. Winkler, T. J. Plona, B. J. Landsberger, and D. L. Johnson, "Test of hyperelasticity in highly nonlinear solids: Sedimentary rocks," Phys. Rev. Lett., vol. 93, p. 214301, Nov. 2004.
20. X. Jacob, C. Barrière, and D. Royer, "Acoustic nonlinearity parameter measurements in solids using the collinear mixing of elastic waves," Appl. Phys. Lett., vol. 82, pp. 886-888, Feb. 2003.
21. V. Chiroiu, P. P. Delsanto, L. Munteanu, C. Rugina, and M. Scalerandi, "Determination of the second- and third-order elastic constants in Al from the natural frequencies," J. Acoust. Soc. Amer., vol. 102, pp. 193-198, July 1997.
22. W. H. Prosser and R. E. Green, Jr., "Characterization of the nonlinear properties of graphite/epoxy composite using ultrasound," J. Reinforced Plastics Composites, vol. 9, pp. 162-173, 1990.
23. X. Xu, F. Mao, X. Gong, and D. Zhang, "Theoretical calculation and experimental study on the third-order nonlinearity parameter C/A for organic liquids and biological fluids," J. Acoust. Soc. Amer., vol. 113, pp. 1743-1748, Mar. 2003.
24. D. Gerlich, "Fourth-order elastic moduli of diamond structure materials," J. Appl. Phys., vol. 77, pp. 4373-4379, May 1995.
25. M. F. Hamilton, Y. A. Ilinskii, and E. A. Zabolotskaya, "Separation of compressibility and shear deformation in the elastic energy density (L)," J. Acoust. Soc. Amer., vol. 116, pp. 41-44, July 2004.
26. E. A. Zabolotskaya, M. F. Hamilton, Y. A. Ilinskii, and G. D. Meegan, "Modeling of nonlinear shear waves in soft solids," J. Acoust. Soc. Amer., vol. 116, pp. 2807-2813, Nov. 2004.
27. H. F. Tiersten and A. Ballato, "Nonlinear extensional vibrations of quartz rods," J. Acoust. Soc. Amer., vol. 73, pp. 2022-2033, June 1983.
28. D. J. Steigmann and M. G. Faulkner, "Variational theory of spatial rods," J. Elasticity, vol. 33, pp. 1-26, Oct. 1993.
29. A. V. Porubov and G. A. Maugin, "Longitudinal strain solitary waves in presence of cubic non-linearity," Int. J. Non-Linear Mech., vol. 40, pp. 1041-1048, Sep. 2005.
30. C. Campos-Pozuelo, "Estudio del comportamiento nolineal de materiales metálicos sometidos a vibraciones ultrasónicas de alta intensidad," Ph.D. thesis, Universidad Complutense de Madrid, 1994. (in Spanish)
31. A. S. Nowick, "Anelasticity: An introduction," in Physical Acoustics. vol. XIII, W. P. Mason and R. N. Thurston, Eds. New York: Academic, 1977, pp. 1-28.
32. C. Vanhille and C. Campos-Pozuelo, "A numerical formulation for nonlinear ultrasonic waves propagation in fluids," Ultrasonics, vol. 42, pp. 1123-1128, Aug. 2004.
33. L. Lapidus and G. F. Pinder, Numerical Solution of Partial Differential Equations in Science and Engineering. New York: Wiley-Interscience, 1999.
34. J. van Randeraat and R. E. Stterington, Eds. Piezoelectric Ceramics. London: Mullard Ltd., 1974.
35. W. P. Mason, "Internal friction measurements in solids," in Low and High-Amplitude Internal-Friction Measurements in Solids and Their Relation to Imperfection Motions. C. J. Mahon, Jr., Ed. New York: Interscience, 1968, pp. 288-382.