Experimental and Numerical Study of Nonlinear Lamb Waves of a Low-Frequency S0 Mode in Plates with Quadratic Nonlinearity
Abstract
:1. Introduction
2. Nonlinear Lamb Waves
3. Numerical Simulation
4. Experimental Measurement
5. Result Discussion
5.1. Fundamental Waves and Second Harmonics
5.2. The Influence of Frequency-Thickness
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Szilard, J. Ultrasonic Testing: Nonconventional Testing Techniques; John Wiley & Sons Ltd.: New York, NY, USA, 1982. [Google Scholar]
- Blitz, J.; Simpson, G. Ultrasonic Methods of Non-Destructive Testing; Springer Nature: Berlin, Germany, 1995. [Google Scholar]
- Drinkwater, B.W.; Wilcox, P.D. Ultrasonic arrays for non-destructive evaluation: A review. NDT E Int. 2006, 39, 525–541. [Google Scholar] [CrossRef]
- Cantrell, J.H.; Yost, W.T. Nonlinear ultrasonic characterization of fatigue microstructures. Int. J. Fatigue 2001, 23, 487–490. [Google Scholar] [CrossRef]
- Ogi, H.; Hirao, M.; Aoki, S. Noncontact monitoring of surface-wave nonlinearity for predicting the remaining life of fatigued steels. J. Appl. Phys. 2001, 90, 438–442. [Google Scholar] [CrossRef]
- Nagy, P.B. Fatigue damage assessment by nonlinear ultrasonic materials characterization. Ultrasonics 1998, 36, 375–381. [Google Scholar] [CrossRef]
- Donskoy, D.; Zagrai, A.; Chudnovsky, A.; Golovin, E.; Agarwala, V.S. Assessment of incipient material damage and remaining life prediction with nonlinear acoustics. J. Acoust. Soc. Am. 2006, 119, 3293. [Google Scholar] [CrossRef]
- Li, W.; Cho, Y.; Achenbach, J.D. Detection of thermal fatigue in composites by second harmonic Lamb waves. Smart Mater. Struct. 2012, 21, 85–93. [Google Scholar] [CrossRef]
- Biwa, S.; Nakajima, S.; Ohno, N. On the acoustic nonlinearity of solid-solid contact with pressure-dependent interface stiffness. J. Appl. Mech. 2004, 71, 508–515. [Google Scholar] [CrossRef]
- Cantrell, J.H. Fundamentals and applications of nonlinear ultrasonic nondestructive evaluation. In Ultrasonic Nondestructive Evaluation; CRC Press: Boca Raton, FL, USA, 2004; pp. 363–434. [Google Scholar]
- Chillara, V.K.; Lissenden, C.J. Nonlinear guided waves in plates: A numerical perspective. Ultrasonics 2014, 54, 1553–1558. [Google Scholar] [CrossRef] [PubMed]
- Shen, Y.; Giurgiutiu, V. WaveFormRevealer: An analytical framework and predictive tool for the simulation of multi-modal guided wave propagation and interaction with damage. Struct. Health Monit. 2014, 13, 491–511. [Google Scholar] [CrossRef]
- Shen, Y.; Giurgiutiu, V. Predictive modeling of nonlinear wave propagation for structural health monitoring with piezoelectric wafer active sensors. J. Intell. Mater. Syst. Struct. 2014, 25, 506–520. [Google Scholar] [CrossRef]
- Solodov, I.Y.; Krohn, N.; Busse, G. CAN: An example of nonclassical acoustic nonlinearity in solids. Ultrasonics 2002, 40, 621–625. [Google Scholar] [CrossRef]
- Lu, Y.; Ye, L.; Su, Z.; Yang, C. Quantitative assessment of through-thickness crack size based on Lamb wave scattering in aluminium plates. NDT E Int. 2008, 41, 59–68. [Google Scholar] [CrossRef]
- Shen, Y.; Cesnik, C.E.S. Modeling of nonlinear interactions between guided waves and fatigue cracks using local interaction simulation approach. Ultrasonics 2016, 74, 106–123. [Google Scholar] [CrossRef] [PubMed]
- Deng, M.-X.; Yang, J. Characterization of elastic anisotropy of a solid plate using nonlinear Lamb wave approach. J. Sound Vib. 2007, 308, 201–211. [Google Scholar] [CrossRef]
- Deng, M.; Xiang, Y.; Liu, L. Time-domain analysis and experimental examination of cumulative second-harmonic generation by primary Lamb wave propagation. J. Appl. Phys. 2011, 109, 113525. [Google Scholar] [CrossRef]
- Matsuda, N.; Biwa, S. Phase and group velocity matching for cumulative harmonic generation in Lamb waves. J. Appl. Phys. 2011, 109, 094903. [Google Scholar] [CrossRef] [Green Version]
- Li, M.; Deng, M.; Gao, G.; Xiang, Y. Mode pair selection of circumferential guided waves for cumulative second-harmonic generation in a circular tube. Ultrasonics 2018, 82, 171–177. [Google Scholar] [CrossRef] [PubMed]
- Matlack, K.H.; Kim, J.-Y.; Jacobs, L.J.; Qu, J. Experimental characterization of efficient second harmonic generation of Lamb wave modes in a nonlinear elastic isotropic plate. J. Appl. Phys. 2011, 109, 014905. [Google Scholar] [CrossRef]
- Li, M.; Deng, M.; Gao, G.; Xiang, Y. Modeling of second-harmonic generation of circumferential guided wave propagation in a composite circular tube. J. Sound Vib. 2018, 421, 234–245. [Google Scholar] [CrossRef]
- Bermes, C.; Kim, J.Y.; Qu, J.; Jacobs, L.J. Experimental characterization of material nonlinearity using Lamb waves. Appl. Phys. Lett. 2007, 90, 021901. [Google Scholar] [CrossRef]
- Bermes, C.; Kim, J.-Y.; Qu, J.; Jacobs, L.J. Nonlinear Lamb waves for the detection of material nonlinearity. Mech. Syst. Signal Process. 2008, 22, 638–646. [Google Scholar] [CrossRef]
- Müller, M.F.; Kim, J.-Y.; Qu, J.; Jacobs, L.J. Characteristics of second harmonic generation of Lamb waves in nonlinear elastic plates. J. Acoust. Soc. Am. 2010, 127, 2141–2152. [Google Scholar] [CrossRef] [PubMed]
- Matlack, K.H.; Kim, J.Y.; Jacobs, L.J.; Qu, J. Review of second harmonic generation measurement techniques for material state determination in metals. J. Nondestruct. Eval. 2015, 34, 273. [Google Scholar] [CrossRef]
- Wan, X.; Tse, P.W.; Xu, G.H.; Tao, T.F.; Zhang, Q. Analytical and numerical studies of approximate phase velocity matching based nonlinear S0 mode Lamb waves for the detection of evenly distributed microstructural changes. Smart Mater. Struct. 2016, 25, 045023. [Google Scholar] [CrossRef]
- Zuo, P.; Zhou, Y.; Fan, Z. Numerical and experimental investigation of nonlinear ultrasonic Lamb waves at low frequency. Appl. Phys. Lett. 2016, 109, 021902. [Google Scholar] [CrossRef]
- Castaings, M.; Le Clezio, E.; Hosten, B. Modal decomposition method for modeling the interaction of Lamb waves with cracks. J. Acoust. Soc. Am. 2002, 112, 2567–2582. [Google Scholar] [CrossRef] [PubMed]
- Liu, X.F.; Bo, L.; Liu, Y.L.; Zhao, Y.X.; Zhang, J.; Hu, N.; Fu, S.Y.; Deng, M.X. Detection of micro-cracks using nonlinear lamb waves based on the Duffing-Holmes system. J. Sound Vib. 2017, 405, 175–186. [Google Scholar] [CrossRef]
- Jiao, J.; Meng, X.; He, C.; Wu, B. Nonlinear Lamb wave-mixing technique for micro-crack detection in plates. NDT E Int. 2016, 85, 63–71. [Google Scholar]
- Ishii, Y.; Biwa, S.; Adachi, T. Non-collinear interaction of guided elastic waves in an isotropic plate. J. Sound Vib. 2018, 419, 390–404. [Google Scholar] [CrossRef]
- Li, F.; Zhao, Y.; Cao, P.; Hu, N. Mixing of ultrasonic Lamb waves in thin plates with quadratic nonlinearity. Ultrasonics 2018, 87, 33–43. [Google Scholar] [CrossRef] [PubMed]
- Zhu, W.; Xiang, Y.; Liu, C.-J.; Deng, M.; Ma, C.; Xuan, F.-Z. Fatigue damage evaluation using nonlinear Lamb Waves with Quasi phase-velocity matching at low frequency. Materials 2018, 11, 1920. [Google Scholar] [CrossRef] [PubMed]
- Hasanian, M.; Lissenden, C.J. Second order harmonic guided wave mutual interactions in plate: Vector analysis, numerical simulation, and experimental results. J. Appl. Phys. 2017, 122, 084901. [Google Scholar] [CrossRef]
- Liu, X.; Bo, L.; Liu, Y.; Zhao, Y.; Zhang, J.; Deng, M.; Hu, N. Location identification of closed crack based on Duffing oscillator transient transition. Mech. Syst. Signal Process. 2018, 100, 384–397. [Google Scholar] [CrossRef]
- Radecki, R.; Su, Z.; Cheng, L.; Packo, P.; Staszewski, W.J. Modelling nonlinearity of guided ultrasonic waves in fatigued materials using a nonlinear local interaction simulation approach and a spring model. Ultrasonics 2018, 84, 272–289. [Google Scholar] [CrossRef]
- Liu, Y.; Kim, J.-Y.; Jacobs, L.J.; Qu, J.; Li, Z. Experimental investigation of symmetry properties of second harmonic Lamb waves. J. Appl. Phys. 2012, 111, 053511. [Google Scholar] [CrossRef]
- Zhao, Y.; Chen, Z.; Cao, P.; Qiu, Y. Experiment and FEM study of one-way mixing of elastic waves with quadratic nonlinearity. NDT E Int. 2015, 72, 33–40. [Google Scholar] [CrossRef]
- Lima, W.J.N.D.; Hamilton, M.F. Finite-amplitude waves in isotropic elastic plates. J. Sound Vib. 2003, 265, 819–839. [Google Scholar] [CrossRef]
- Zhao, Y.X.; Li, F.L.; Cao, P.; Liu, Y.L.; Zhang, J.Y.; Fu, S.Y.; Zhang, J.; Hu, N. Generation mechanism of nonlinear ultrasonic Lamb waves in thin plates with randomly distributed micro-cracks. Ultrasonics 2017, 79, 60–67. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Sun, X.; Ding, X.; Li, F.; Zhou, S.; Liu, Y.; Hu, N.; Su, Z.; Zhao, Y.; Zhang, J.; Deng, M. Interaction of Lamb wave modes with weak material nonlinearity: Generation of symmetric zero-frequency mode. Sensors 2018, 18, 2451. [Google Scholar] [CrossRef] [PubMed]
ρ (kg/m3) | λ (MPa) | μ (MPa) | l (MPa) | m (MPa) | n (MPa) |
---|---|---|---|---|---|
2704 | 5.11 × 104 | 2.63 × 104 | −2.82 × 105 | −3.39 × 105 | −4.16 × 105 |
Case | L/mm (Numerical Simulations) | L/mm (Experiments) | Error |
---|---|---|---|
f = 300 kHz, h = 2.0 mm | 180 | 175 | 2.8% |
f = 300 kHz, h = 2.5 mm | 100 | 125 | 25% |
f =240 kHz, h = 2.5 mm | 240 | 250 | 4.2% |
f = 200 kHz, h = 2.0 mm | 800 | 700 | 12.5% |
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Ding, X.; Zhao, Y.; Hu, N.; Liu, Y.; Zhang, J.; Deng, M. Experimental and Numerical Study of Nonlinear Lamb Waves of a Low-Frequency S0 Mode in Plates with Quadratic Nonlinearity. Materials 2018, 11, 2096. https://doi.org/10.3390/ma11112096
Ding X, Zhao Y, Hu N, Liu Y, Zhang J, Deng M. Experimental and Numerical Study of Nonlinear Lamb Waves of a Low-Frequency S0 Mode in Plates with Quadratic Nonlinearity. Materials. 2018; 11(11):2096. https://doi.org/10.3390/ma11112096
Chicago/Turabian StyleDing, Xiangyan, Youxuan Zhao, Ning Hu, Yaolu Liu, Jun Zhang, and Mingxi Deng. 2018. "Experimental and Numerical Study of Nonlinear Lamb Waves of a Low-Frequency S0 Mode in Plates with Quadratic Nonlinearity" Materials 11, no. 11: 2096. https://doi.org/10.3390/ma11112096