Multi-mode nonlinear resonance ultrasound spectroscopy for defect imaging: An analytical approach for the one-dimensional case

Journal of the Acoustical Society of America

Volumn 122, Issue 1, 2007, Pages 73-90

  Van Den Abeele, Koen ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

HYSTERESIS; IMAGING SYSTEMS; NATURAL FREQUENCIES; NONLINEAR EQUATIONS; NUMERICAL METHODS; VIBRATION ANALYSIS;

EXCITATION MODES; RESONANCE ULTRASOUND SPECTROSCOPY (RUS); VIBRATION PATTERNS;

ULTRASONICS;

AMPLITUDE MODULATION; ARTICLE; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; PRIORITY JOURNAL; SIMULATION; SPECTROSCOPY; ULTRASOUND; COMPUTER SIMULATION; ELASTICITY; EQUIPMENT; MATERIALS TESTING; MECHANICAL STRESS; METHODOLOGY; NONLINEAR SYSTEM; REPRODUCIBILITY; STATISTICAL MODEL; VIBRATION;

COMPUTER SIMULATION; ELASTICITY; EQUIPMENT FAILURE ANALYSIS; LINEAR MODELS; MATERIALS TESTING; NONLINEAR DYNAMICS; REPRODUCIBILITY OF RESULTS; STRESS, MECHANICAL; ULTRASONICS; VIBRATION;

EID: 34547469122     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.2735807     Document Type: Article

References (48)

1. Aleshin, V., Gusev, V., and Zaitsev, V. Y. (2004). " Propagation of acoustics waves of nonsimplex form in a material with hysteretic quadratic nonlinearity: Analysis and numerical simulations., " J. Comput. Acoust. 12 (3), 319-354.
2. Antonets, V. A., Donskoy, D. M., Sutin, A. M. (1986). " Nonlinear vibro-diagnostics of flaws in multilayered structures., " Mech. Compos. Mater. 15, 934-937.
3. Ballad, E., Vezirov, S., Pfleiderer, K., Solodov, I., and Busse, G. (2004). " Nonlinear modulation technique for NDE with air-coupled ultrasound., " Ultrasonics 42 (1-9), 1031-1036.
4. Cantrell, J. H., and Yost, W. T. (1994). " Acoustic harmonic-generation from fatigue-induced dislocation dipoles., " Philos. Mag. A 69, 315-326.
5. Capogrosso-Sansone, B., and Guyer, R. A. (2002). " Dynamic model of hysteretic elastic systems., " Phys. Rev. B 66, 224101.
6. Delsanto, P. P., Gliozzi, A. S., Hiresekorn, M., and Nobili, M. (2006). " A 2D spreing model for the simulation of ultrasonic wave propagation in nonlinear hysteretic media., " Ultrasonics 44, 279-286.
7. Gliozzi, A. S., Nobili, M., and Scalerandi, M. (2006). " Modelling localized nonlinear damage and analysis of its influence on resonance frequencies., " J. Phys. D 39 (17), 3985-3903.
8. Gusev, V. (2000). " Propagation of acoustic pulses in material with hysteretic nonlinearity., " J. Acoust. Soc. Am. 107 (6), 3047-3058.
9. Guyer, R. A., McCall, K. R., and Van Den Abeele, K. (1998). " Slow elastic dynamics in a resonant bar of rock., " Geophys. Res. Lett. 25 (10), 1585-1588.
10. Ichitsubo, T., Ogi, H., Hirao, M., Tanaka, K., Osawa, M., Yokokawa, T., Kobayashi, T., and Harada, H. (2002). " Elastic constant measurement of Ni-base superalloy with the RUS and mode selective EMAR methods., " Ultrasonics 40, 211-215.
11. Johnson, P. A., and Sutin, A. M. (2005) " Slow dynamics and anomalous nonlinear fast dynamics in diverse solids., " J. Acoust. Soc. Am. 117 (1), 124-130.
12. Johnson, P. A., Zinszner, B., and Rasolofosaon, P. N. J. (1996). " Resonance and elastic nonlinear phenomena in rock., " J. Geophys. Res. 101, 11553-11564.
13. Kac, M. (1966). " Can one hear the shape of a drum? " Am. Math. Monthly 10.2307/2313748 73, 1-23.
14. Kazakov, V. V., Sutin, A. M., and Johnson, P. A. (2002). " Sensitive imaging of an elastic nonlinear wave-scattering source in a solid., " Appl. Phys. Lett. 81 (4), 646-648.
15. Keppens, V., Mandrus, D., Sales, B. C., Chakoumakos, B. C., Dai, P., Coldea, R., Maple, M. B., Gajewski, D. A., Freeman, E. J., and Bennington, S. (1998). " Localized vibrational modes in metallic solids., " Nature (London) 395 (6705), 876-878.
16. Krohn, N., Stoessel, R., and Busse, G. (2002). " Acoustic non-linearity for defect selective imaging., " Ultrasonics 40 (1-8), 633-637.
17. Landau, L. E., and Lifshitz, E. (1969). Mechanics (Oxford, Pergamon).
18. Leonard, K. R., Malyarenko, E. V., and Hinders, M. K. (2002). " Ultrasonic lamb wave tomography., " Inverse Probl. 18, pp. 1795-1808.
19. Maynard, J. (1996). " Resonant ultrasound spectroscopy., " Phys. Today 49, 26-31.
20. McCall, K. R. (1994). " Theoretical-study of nonlinear elastic-wave propagation., " J. Geophys. Res., [Solid Earth] 99 (B2), 2591-2600.
21. McCall, K. R., and Guyer, R. A. (1994). " Equation of state and wave-propagation in hysteretic nonlinear elastic-materials., " J. Geophys. Res., [Solid Earth] 99 (B12), 23887-23897.
22. McCall, K. R., and Guyer, R. A. (1996). " A new theoretical paradigm to describe hysteresis, discrete memory and nonlinear elastic wave propagation in rock., " Nonlinear Processes Geophys. 3, 89-101.
23. Michaels, J. E., and Michaels, T. E. (2006). " Enhanced differential methods for guided wave phased array imaging using spatially distributed piezoelectric transducers., " Rev. Prog. Quant. Nondestr. Eval. 25A, 837-844.
24. Migliori, A., and Sarrao, J. L. (1997) Resonant Ultrasound Spectroscopy: Applications to Physics, Materials Measurements, and Non-destructive Evaluation (Wiley, New York).
25. Morris, W. L., Buck, O., and Inman, R. V. (1979). " Acoustic harmonic-generation due to fatigue damage in high-strength aluminum., " J. Appl. Phys. 50 (11), 6737-6741.
26. Nagy, P. B. (1998). " Fatigue damage assessment by nonlinear ultrasonic materials characterization., " Ultrasonics 36 (1-5), 375-381.
27. Nakamura, N., Ogi, H., and Hirao, M. (2004). " Resonance ultrasound spectroscopy with laser-Doppler interferometry for studying elastic properties of thin films., " Ultrasonics 42 (1-9), 491-494.
28. Nayfeh, A. (1973). Perturbation Methods (Wiley, New York).
29. Nazarov, V. E., Ostrovsky, L. A., Soustova, I., and Sutin, A. M. (1988). " Nonlinear acoustics of microinhomogeneous media., " Phys. Earth Planet. Inter. 50 (1), 65-73.
30. Nazarov, V. E., and Sutin, A. M. (1989). " Theory of parametric sound receiver using a nonlinear layer., " Sov. Phys. Acoust. 35, 510-512.
31. Ogi, H., Sato, K., Asada, T., and Hirao, M. (2002). " Complete mode identification for resonance ultrasound spectroscopy., " J. Acoust. Soc. Am. 112 (6), 2553-2557.
32. Pohit, G., Mallik, A., and Venkatesan, C. (1999). " Free out-of-plane vibrations of a rotating beam with non-linear elastomeric constraints., " J. Sound Vib. 220 (1), 1-25.
33. Scalerandi, M., Agostini, V., Delsanto, P. P., Van Den Abeele, K., and Johnson, P. A. (2003). " Local interaction simulation approach to modelling nonclassical, nonlinear elastic behavior in solids., " J. Acoust. Soc. Am. 113 (6), 3049-3059.
34. Stoessel, R., Krohn, N., Pfleiderer, K., and Busse, G. (2002). " Air-coupled ultrasound inspection of various materials., " Ultrasonics 40 (1-8), 159-163.
35. Sutin, A. M., and Donskoy, D. M. (1998). " Vibro-acoustic modulation nondestructive evaluation technique., " Proc. SPIE 3397, 226-237.
36. Teklu, A., Ledbetter, H., Kim, S., Boatner, L. A., Keppens, V., and McGuire, M. (2004). " Single crystal elastic constants of 70Fe-15Ni-15Cr alloy., " Metall. Mater. Trans. A 35, 3149-3153.
37. TenCate, J. A., and Shankland, T. J. (1996). " Slow dynamics in the nonlinear elastic response of Berea sandstone., " Geophys. Res. Lett. 23 (21), 3019-3022.
38. TenCate, J. A., Smith, E., and Guyer, R. A. (2000) " Universal slow dynamics in granular solids., " Phys. Rev. Lett. 85 (5), 1020-1023.
39. Ulrich, T., McCall, K. R., and Guyer, R. A. (2002). " Determination of elastic moduli of rock samples using resonant ultrasound spectroscopy., " J. Acoust. Soc. Am. 111 (4), 1667-1674.
40. Van Den Abeele, K., and Johnson, P. A. (1996). " Elastic pulsed wave propagation in media with second- or higher-order nonlinearity. II. Simulation of experimental measurements on Berea sandstone., " J. Acoust. Soc. Am. 99 (6), 3346-3352.
41. Van Den Abeele, K., Johnson, P. A., Guyer, R. A., and McCall, K. R. (1997). " On the quasi-analytic treatment of hysteretic nonlinear response in elastic wave propagation., " J. Acoust. Soc. Am. 101 (4), 1885-1898.
42. Van Den Abeele, K., Johnson, P. A., and Sutin, A. M. (2000a). " Nonlinear elastic wave spectroscopy (NEWS) techniques to discern material damage, part I: Nonlinear wave modulation spectroscopy (NWMS)., " Res. Nondestruct. Eval. 12 (1), 17-30.
43. Van Den Abeele, K., Carmeliet, J., TenCate, J. A., and Johnson, P. A. (2000b). " Nonlinear Elastic Wave Spectroscopy (NEWS) techniques to discern material damage. Part II: Single Mode Nonlinear Resonant Acoustic Spectroscopy (SIMONRAS)., " Res. Nondestruct. Eval. 12 (1), 31-42.
44. Van Den Abeele, K., and De Visscher, J. (2000). " Damage assessment in reinforced concrete using spectral and temporal nonlinear vibration techniques., " Cem. Concr. Res. 30 (9), 1453-1464.
45. Van Den Abeele, K., Van De Velde, K., and Carmeliet, J. (2001). " Inferring the degradation of pultruded composites from dynamic nonlinear resonance measurements., " Polym. Compos. 22 (4), 555-567.
46. Van Den Abeele, K., Schubert, F., Aleshin, V., Windels, F., and Carmeliet, J. (2004). " Resonant bar simulations in media with localized damage., " Ultrasonics 42, 1017-1024.
47. Visscher, W., Migliori, A., Bell, T., and Reinert, R. (1991). " On the normal modes of free vibration of inhomogeneous and anisotropic elastic objects., " J. Acoust. Soc. Am. 90 (4), 2154-2162.
48. Zimenkov, S., and Nazarov, V. (1995). " Propagation of nonlinear acoustic waves in rocks., " Izv., Acad. Sci., USSR, Phys. Solid Earth 30 (5), 437-439.