Nonlinear Response of a Weakly Damaged Metal Sample: A Dissipative Modulation Mechanism of Vibro-Acoustic Interaction

Abstract

The nonlinear vibro-acoustic response of solid samples containing quite a small amount of defects can be anomalously high in magnitude compared to the case of undamaged intact solids. Functional de pendencies of the nonlinear effects exhibit rather interesting behavior. In this paper, experimental results on nonlinearity-induced cross-modulation of a high-frequency (HF) f = 15 — 30 kHz signal by a low-frequency (LF) F = 20 - 60 Hz vibration in an aluminum plate with a small single crack are reported. Comparison with a reference sample (the identical plate without a crack) has proven that the presence of such a small defect can be easily detected due to its nonlinear manifestations. It is demonstrated that under proper choice of the sounding signal parameters, the effect level can be so pronounced that the amplitude of the modulation side-lobes originated due to the nonlinearity exceeds the amplitude of the fundamental harmonic of the HF signal. Main functional features of the observed phenomena are analyzed, and a new physical explana tion is suggested based on a dissipative mechanism of vibro-acoustic interaction. Results of the numerical simulation of the effect are also presented.

Keywords

Nonlinear response nonlinear vibro-acoustics diagnostics cracks

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References

Antonets, V.A. , Donskoy, D.M. , and Sutin, A.M. , 1986, "Nonlinear vibrodiagnostics of delayer in layer construction," Mechanics of Composite Materials 5, 934-937 (in Russian).

Collacott, R.A. , 1985, Structural Integrity Monitoring, Chapman & Hall, London, UK.

Ekimov, A.E. , Didenkulov, I.N. , and Kazakov, V.V. , 1998, "Nonlinear acoustic phenomena in a rod with a crack," in Proceedings of the 3rd International Conference of Acoustical and Vibratory Surveillance, Senlis, France, pp. 481-489.

Fritzen, C.P. , Jennewein, D. , and Kiefer, T. , 1998, "Damage detection based on model updating methods," Mechanical Systems and Signal Processing 12(1), 163-186.

Johnson, P.A. and Rasolofosaon, P.N.J. , 1996, "Manifestation of nonlinear elasticity in rock: Convincing evidence over large frequency and strain intervals from laboratory studies," Nonlinear Processes in Geophysics 3, 77-88.

Johnson, P.A. , Sutin, A. , and Van Den Abeele, K. E-A., 1999, "Application of nonlinear wave modulation spectroscopy to discern material damage," in Proceedings of the 2nd International Conference, Emerging Technologies in NDT, Athens, Greece, May

Korotkov, A.S. and Sutin, A.M. , 1994, "Modulation of ultrasound by vibrations in metal constructions with cracks," Acoustics Letters 18, 59-62.

Landau, L.D. and Lifshitz, E.M. , 1986, Theory of Elasticity, Pergamon , Elmsford, NY

Naugolnykh, K. and Ostrovsky, L. , 1998, Nonlinear Wave Processes in Acoustics , Cambridge University Press, Cambridge, UK.

10.

Nazarov, V.E. , 1994, "Self-action of elastic waves in media with dissipative nonlinearity," Acoustics Letters 17(8), 145-149.

11.

Nazarov, V.E. , Ostrovsky, L.A. , Soustova, I.A. , and Sutin, A.M. , 1988, "Nonlinear acoustics of micro-inhomogeneous media," Physics of the Earth and Planetary Interiors 50(1), 65-73.

12.

Nazarov, V.E. and Zimenkov, S.V. , 1993, "Sound by sound modulation in metallic resonators," Acoustics Letters 16(9), 198-201.

13.

Richardson, M. and Mannan, M.A. , 1992, "Remote detection and location of structural faults using modal parameters," in Proceedings of 10th International Conference on Modal Analysis (IMAC), San Diego, CA, September, pp. 502-507.

14.

Rudenko, O.V. , 1993, "Nonlinear methods of acoustical diagnostics," Defectoscopia 8 , 24-32(in Russian).

15.

Sutin, A.M. , 1992, "Nonlinear acoustic diagnostics of micro-inhomogeneous media," in Proceedings of the International Symposium on Recent Advances in Surveillance Using Acoustical and Vibrational Methods , Senlis, France, pp. 497-506.

16.

Sutin, A.M. , Korotkov, A.S. , Didenkulov, I.N. , Kim, E.J. , and Yoon, S.W. , 1995, "Nonlinear acoustic methods for crack and fatigue detection," in Proceedings of Physical Acoustic Workshop, Safety Diagnostics of Underwater Constructions by Using Acoustics , Kaist, Seoul Branch, Seoul, Korea, pp. 43-55.

17.

Van Den Abeele, K.E.A. , Carmeliet, J. , TenCate, J.A. , and Johnson, P.A. , 1999, "Single mode nonlinear resonant acoustic spectroscopy (SIMONRAS) for damage detection in quasi-brittle materials," in Proceedings of the 2nd International Conference, Emerging Technologies in NDT , Athens, Greece, May.

18.

Zaitsev, V. Yu. , 1996, "A model of anomalous acoustic nonlinearity of microinhomogeneous media," Acoustics Letters 19(9), 171-176.

19.

Zaitsev, V. Yu. , 1998, "Nonlinear acoustic manifestations as an informative sign of structural changes in non-destructive interrogation problems," in Proceedings of the 3rd International Conference Acoustical and Vibratory Surveillance, Senlis, France , pp. 409-418.

20.

Zaitsev, V. Yu. , Sutin A.M. , Belyaeva I. Yu. , and Nazarov V.E. , 1995, "Nonlinear interaction of acoustical waves due to cracks and its possible usage for cracks detection," Journal of Vbration and Control 1(3), 335-344.