Abstract
In this paper, the effect of local defect resonance (LDR) on the nonlinear ultrasonic responses of defects is studied and applied for enhancement of sensitivity of nonlinear NDE. Unlike the resonance of the whole specimen, the LDR provides an efficient energy pumping from the wave directly to the defect and causes an efficient generation of the higher harmonics and wave mixing even at moderate input signals. At higher levels of excitation, a combined effect of LDR and nonlinearity results in qualitatively new “nonclassical” features characteristic of the nonlinear and parametric resonances. The resonant nonlinear defects demonstrate threshold dynamics of instable vibrations, hysteresis, super- and subharmonic resonances. Under nonlinear LDR conditions nearly total input energy can be converted into higher harmonic or subharmonic vibrations of the defect. This proposes nonlinear LDR application as an extremely efficient and sensitive mode for nonlinear imaging and NDE.
Similar content being viewed by others
References
Breazeale, M.A., Philip, J.: Determination of third-order elastic constants from higher harmonic generation. In: Mason, W.P. (ed.) Physical Acoustics, v. XVII. Academic Press, New York (1965)
Zarembo, L.K., Krasilnikov, V.A.: Nonlinear phenomena in the propagation of elastic waves in solids. Soviet Physics Uspekhi 13, 778–797 (1971)
Gedroitz, A.A., Krasilnikov, V.A.: Elastic waves of finite amplitude and deviations from Hooke‘s law. Sov. Phys. JETP. 16, 1122 (1963)
Yost, W.T., Cantrell, J.H.: Materials characterization using acoustic nonlinearity parameters and harmonic generation: engineering materials. Rev. Prog. Quant. Nondestr. Eval. 9, 1669–1676 (1990)
Cantrell, J.H., Yost, W.T.: Effect of precipitate coherency strains on acoustic harmonic generation. J. Appl. Phys. 81, 2957 (1997)
Buck, O., Morris, W.M., Richardson, J.M.: Acoustic harmonic generation at unbounded interfaces and fatigue cracks. Appl. Phys. Lett. 33, 371–373 (1978)
Len, K.S., Severin, F.M.: Experimental observation of Influence of contact nonlinearity on the reflection of bulk acoustic waves and propagation of surface acoustic waves. Sov. Phys. Acoust. 37, 610–612 (1991)
Solodov, I.: Ultrasonics of nonlinear contacts: propagation, reflection and NDE-applications. Ultrasonics 36, 383–390 (1998)
Solodov, I., Krohn, N., Busse, G.: CAN: an example of nonclassical nonlinearity in solids. Ultrasonics 40, 621–625 (2002)
Ballad, E.M., Korshak, B.A., Solodov, I., Busse, G.: Local nonlinear and parametric effects for non-bonded contacts in solids. In: Proceedings 16th ISNA, pp. 727–734, Moscow (2002)
Solodov, I., Korshak, B.: Instability, chaos, and memory in acoustic wave–crack interaction. Phys. Rev. Lett. 88, 014303 (2002)
Solodov, I., Wackerl, J., Pfleiderer, K., Busse, G.: Nonlinear self-modulation and subharmonic acoustic spectroscopy for damage detection and location. Appl. Phys. Lett. 84, 5386–5388 (2004)
Solodov, I., Bai, J., Bekgulyan, S., Busse, G.: A local defect resonance to enhance acoustic wave-defect interaction in ultrasonic nondestructive testing. Appl. Phys. Lett. 99, 211911 (2011)
Solodov, I., Bai, J., Busse, G.: Resonant ultrasound spectroscopy of defects: case study of flat-bottomed holes. J. Appl. Phys. 113, 223512 (2013)
Minorsky, N.: Nonlinear Oscillations. D. Van Nostrand Co., Princeton (1962)
Landau, L.D., Lifshitz, E.M.: Mechanics. Pergamon Press, Oxford (1960)
McLachlan, N.W.: Theory and applications of mathieu functions. Oxford University Press, London (1951)
Kneubuehl, F.K.: Oscillations and Waves. Springer, Berlin (1997)
Van Den Abeele, K.E.-A., Carmeliet, J., TenCate, J., Johnson, P.: Nonlinear elastic wave spectroscopy (NEWS) techniques to discern material damage, Part II: single-mode nonlinear resonance acoustic spectroscopy. Res. Nondestr. Eval. 12, 31–42 (2000)
Van Den Abeele, K.E.-A., De Visscher, J.: Damage assessment in reinforced concrete using spectral and temporal nonlinear vibration techniques. Cem. Concr. Res. 30, 1453–1464 (2000)
Johnson, P., Sutin, A.: Slow dynamics and anomalous nonlinear fast dynamics in diverse solids. J. Acoust. Soc. Am. 117, 124–130 (2005)
Acknowledgments
The author acknowledges support of this study by EU FP-7 in the framework of ALAMSA project.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Solodov, I. Resonant Acoustic Nonlinearity of Defects for Highly-Efficient Nonlinear NDE. J Nondestruct Eval 33, 252–262 (2014). https://doi.org/10.1007/s10921-014-0229-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10921-014-0229-9