Browse > Article
http://dx.doi.org/10.12989/sss.2021.28.1.043

Investigation on modulation of multi-frequency ultrasonic waves in structures with quadratic nonlinearity  

Salehi, Hamid (New Technologies Research Center, Amirkabir University of Technology)
Shamshirsaz, Mahnaz (New Technologies Research Center, Amirkabir University of Technology)
Aghdam, Mohammad Mohammadi (Mechanical Engineering Department, Amirkabir University of Technology)
Publication Information
Smart Structures and Systems / v.28, no.1, 2021 , pp. 43-53 More about this Journal
Abstract
In this study, the modulation of multiple frequency content of a single ultrasonic wave in nonlinear structures is investigated analytically, numerically and experimentally. An experimental technique is proposed based on nonlinear lamb wave propagation in aluminum bars using piezoelectric wafer active sensors (PWAS) to study intrinsic nonlinearity of structures. First, a one-dimensional analytical procedure is developed to study the modulation of one dimensional wave with multiple-frequency content in isotropic medium with quadratic nonlinearity. This procedure is implemented to study modulation of frequency contents of a well-known tone burst signal in nonlinear medium. Then, predictions obtained by the proposed analytical procedure are compared with the results of finite element model, which show strong correlations. The experimental and analytical results reveal that in excitation with a train of tone burst, due to frequency modulation, some new harmonics including a strong sub harmonic generation with frequency of f0/Np appear in the response. The amplitude of this harmonic is even higher than common second harmonic generation (2f0). This can be seen in the experimental results when the excitation frequencies are correctly selected. Finally, it is explained that, why the new sub harmonic generation is less affected by the nonlinearity induced by the excitation system.
Keywords
distributed damage; frequency modulation; nonlinear medium; PWAS; ultrasonic waves;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 Zhang, Z., Nagy, P.B. and Hassan, W. (2016), "Analytical and numerical modeling of non-collinear shear wave mixing at an imperfect interface", Ultrasonics, 65, 165-176. https://doi.org/10.1016/j.ultras.2015.09.021   DOI
2 Ginzburg, D., Ciampa, F., Scarselli, G. and Meo, M. (2017), "SHM of single lap adhesive joints using subharmonic frequencies", Smart Mater. Struct., 26(10), 105018. https://doi.org/10.1088/1361-665X/aa815c   DOI
3 Hong, X., Ruan, J., Liu, G., Wang, T., Li, Y. and Song, G. (2016), "Synergetics based damage detection of frame structures using piezoceramic patches", Smart Struct. Syst., Int. J., 17(2), 167-194. https://doi.org/10.12989/sss.2016.17.2.167   DOI
4 Huifeng, Z., Liuchen, H., Piaopiao, F., Yuebing, W. and Yonggang, C. (2019), "The study of micro-crack localisation based on vibro-acoustic modulation and time reversal method", Nondestruct. Test. Eval., 34(3), 324-338. https://doi.org/10.1080/10589759.2019.1600687   DOI
5 Jhang, K.Y. (2009), "Nonlinear ultrasonic techniques for nondestructive assessment of micro damage in material: a review", Int. J. Precis. Eng. Manuf., 10(1), 123-135. https://doi.org/10.1007/s12541-009-0019-y   DOI
6 Jingpin, J., Junjun, S., Guanghai, L., Bin, W. and Cunfu, H. (2015), "Evaluation of the intergranular corrosion in austenitic stainless steel using collinear wave mixing method", NDT & E Int., 69, 1-8. https://doi.org/10.1016/j.ndteint.2014.09.001   DOI
7 Jingpin, J., Hongtao, L., Cunfu, H. and Bin, W. (2017b), "Fatigue crack evaluation using the non-collinear wave mixing technique", Smart Mater. Struct., 26(6), 065005. https://doi.org/10.1088/1361-665X/aa6c43   DOI
8 Jeong, H. and Barnard, D. (2011), "Measurements of sub-and super harmonic waves at the interfaces of fatigue-cracked CT specimen", J. Korean Soc. Nondestruct. Test., 31(1), 1-10.
9 Kamas, T., Poddar, B., Lin, B. and Yu, L.L. (2015), "Assessment of temperature effect in structural health monitoring with piezoelectric wafer active sensors", Smart Struct. Syst., Int. J., 16(5), 835-851. http://dx.doi.org/10.12989/sss.2015.16.5.835   DOI
10 Karayannis, C.G., Voutetaki, M.E., Chalioris, C.E., Providakis, C.P. and Angeli, G.M. (2015), "Detection of flexural damage stages for RC beams using piezoelectric sensors (PZT)", Smart Struct. Syst., Int. J., 15(4), 997-1018. https://doi.org/10.12989/sss.2015.15.4.997   DOI
11 Deng, M. and Pei, J. (2007), "Assessment of accumulated fatigue damage in solid plates using nonlinear Lamb wave approach", Appl. Phys. Lett., 90(12), 121902. https://doi.org/10.1063/1.2714333   DOI
12 Klepka, A., Dziedziech, K., Mrowka, J. and Gorski, J. (2019), "Experimental investigation of modulation effects for contacttype interfaces in vibro-acoustic modulation tests", Struct. Health Monitor., 1475921719857624. https://doi.org/10.1177/1475921719857624   DOI
13 Lee, D.J., Cho, Y. and Li, W. (2014), "A feasibility study for Lamb wave mixing nonlinear technique", AIP Conference Proceedings, Vol. 1581, No. 1, pp. 662-666, American Institute of Physics. https://doi.org/10.1063/1.4864883   DOI
14 Li, F., Zhao, Y., Cao, P. and Hu, N. (2018), "Mixing of ultrasonic Lamb waves in thin plates with quadratic nonlinearity", Ultrasonics, 87, 33-43. https://doi.org/10.1016/j.ultras.2018.02.005   DOI
15 Prawin, J. and Rao, A. (2018), "Detection of nonlinear structural behavior using time-frequency and multivariate analysis", Smart Struct. Syst., Int. J., 22(6), 711-725. https://doi.org/10.12989/sss.2018.22.6.711   DOI
16 Pruell, C., Kim, J.Y., Qu, J. and Jacobs, L.J. (2009), "Evaluation of fatigue damage using nonlinear guided waves", Smart Mater. Struct., 18, 035003. https://doi.org/10.1088/0964-1726/18/3/035003   DOI
17 Barnard, D.J., Brasche, L.J.H., Raulerson, D. and Degtyar, A.D. (2003), "Monitoring fatigue damage accumulation with Rayleigh wave harmonic generation measurements", Review of Progress in QNDE, 22, 1393-1400. https://doi.org/10.1063/1.1570294   DOI
18 Croxford, A.J., Wilcox, P.D., Drinkwater, B.W. and Nagy, P.B. (2009), "The use of non-collinear mixing for nonlinear ultrasonic detection of plasticity and fatigue", J. Acoust. Soc. Am., 126(5), EL117-122. https://doi.org/10.1121/1.3231451   DOI
19 Deng, M. (2009), "Cumulative second-harmonic generation of Lamb-mode propagation in a solid plate", J. Appl. Phys., 85, 3051-3058. https://doi.org/10.1063/1.369642   DOI
20 Ding, X., Zhao, Y., Deng, M., Shui, G. and Hu, N. (2020), "One-way Lamb mixing method in thin plates with randomly distributed micro-cracks", Int. J. Mech. Sci., 171, 105371. https://doi.org/10.1016/j.ijmecsci.2019.105371   DOI
21 Jingpin, J., Xiangji, M., Cunfu, H. and Bin, W. (2017a), "Nonlinear Lamb wave-mixing technique for micro-crack detection in plates", NDT & E Int., 85, 63-71. https://doi.org/10.1016/j.ndteint.2016.10.006   DOI
22 Hikata, A., Chick, B.B. and Elbaum, C. (1965), "Dislocation contribution to the second harmonic generation of ultrasonic waves", J. Appl. Phys., 36, 229. https://doi.org/10.1063/1.1713881   DOI
23 Tang, G., Liu, M., Jacobs, L.J. and Qu, J. (2014), "Detecting localized plastic strain by a scanning collinear wave mixing method", J. Nondestruct. Eval., 33(2), 196-204. https://doi.org/10.1007/s10921-014-0224-1   DOI
24 Rajabi, M., Shamshirsaz, M. and Naraghi, M. (2017), "Crack detection in rectangular plate by electromechanical impedance method: modeling and experiment", Smart Struct. Syst., Int. J., 19(4), 361-369. https://doi.org/10.12989/sss.2017.19.4.361   DOI
25 Solodov, I. (2014), "Resonant Acoustic Nonlinearity of Defects for Highly-Efficient Nonlinear NDE", J. Nondestr. Eval., 33(2), 252-262. https://doi.org/10.1007/s10921-014-0229-9   DOI
26 Sun, M., Xiang, Y., Deng, M., Tang, B., Zhu, W. and Xuan, F.Z. (2019), "Experimental and numerical investigations of nonlinear interaction of counter-propagating Lamb waves", Appl. Phys. Lett., 114(1), 011902. https://doi.org/10.1063/1.5061740   DOI
27 Xiang, Y., Deng, M. and Xuan, F.-Z. (2014), "Thermal degradation evaluation of HP40Nb alloy steel after long term service using a nonlinear ultrasonic technique", J. Nondestruct. Eval., 33, 279-287. https://doi.org/10.1007/s10921-013-0222-8   DOI
28 Yang, S., Jung, J., Liu, P., Lim, H.J., Yi, Y., Sohn, H. and Bae, I.H. (2019), "Ultrasonic wireless sensor development for online fatigue crack detection and failure warning", Struct. Eng. Mech., 69(4), 407-416. https://doi.org/10.12989/sem.2019.69.4.407   DOI
29 Yu, L. and Giurgiutiu, V. (2005), "Advanced signal processing for enhanced damage detection with piezoelectric wafer active sensors", Smart Struct. Syst., Int. J., 1(2), 185-215. https://doi.org/10.12989/sss.2005.1.2.185   DOI
30 Zhang, Z., Xu, H., Liao, Y., Su, Z. and Xiao, Y. (2017a), "Vibroacoustic modulation (VAM)-inspired structural integrity monitoring and its applications to bolted composite joints", Compos. Struct., 176, 505-515. https://doi.org/10.1016/j.compstruct.2017.05.043   DOI
31 Zhang, M., Xiao, L., Qu, W. and Lu, Y. (2017b), "Damage detection of fatigue cracks under nonlinear boundary condition using subharmonic resonance", Ultrasonics, 77, 152-159. https://doi.org/10.1016/j.ultras.2017.02.001   DOI
32 Zhao, X., Gao, H., Zhang, G., Ayhan, B., Yan, F., Kwan, C. and Rose, J. (2007), "Active health monitoring of an aircraft wing with embedded piezoelectric sensor/actuator network: I. Defect detection, localization and growth monitoring", Smart Mater. Struct., 16(4), 1208. https://doi.org/10.1088/0964-1726/16/4/032   DOI
33 Zhou, C., Hong, M., Su, Z., Wang, Q. and Cheng, L. (2012), "Evaluation of fatigue cracks using nonlinearities of acoustoultrasonic waves acquired by an active sensor network", Smart Mater. Struct., 22(1), 015018. https://doi.org/10.1088/0964-1726/22/1/015018   DOI
34 Zhao, Y., Chen, Z., Cao, P. and Qiu, Y. (2015), "Experiment and FEM study of one-way mixing of elastic waves with quadratic nonlinearity", NDT & E Int., 72, 33-40. https://doi.org/10.1016/j.ndteint.2015.02.004   DOI
35 Masurkar, F., Tse, P. and Yelve, N.P. (2018), "Evaluation of inherent and dislocation induced material nonlinearity in metallic plates using Lamb waves", Appl. Acoust., 136, 76-85. https://doi.org/10.1016/j.apacoust.2018.02.011   DOI
36 Liu, M., Tang, G., Jacobs, L.J. and Qu, J. (2012), "Measuring acoustic nonlinearity parameter using collinear wave mixing", J. Appl. Phys., 112, 024908. https://doi.org/10.1063/1.4739746   DOI
37 Liu, P., Sohn, H., Yang, S. and Lim, H.J. (2016), "Baseline-free fatigue crack detection based on spectral correlation and nonlinear wave modulation", Smart Mater. Struct., 25(12), 125034. https://doi.org/10.1088/0964-1726/25/12/125034   DOI
38 Malfense-Fierro, G.P. (2014), "Development of nonlinear ultrasound techniques for multidisciplinary engineering applications", Ph.D. Dissertation; University of Bath, Bath, England.
39 Metya, A.K., Tarafder, S. and Balasubramaniam, K. (2018), "Nonlinear Lamb wave mixing for assessing localized deformation during creep", NDT & E Int., 98, 89-94. https://doi.org/10.1016/j.ndteint.2018.04.013   DOI
40 Nagy, P.B., Qu, J. and Jacobs, L.J. (2013), "Finite-size effects on the quasistatic displacement pulse in a solid specimen with quadratic nonlinearity", J. Acoust. Soc. Am., 134(3), 1760-1774. https://doi.org/10.1121/1.4817840   DOI
41 Peng, G., Yuan, S.F. and Xu, X. (2006), "Damage detection on two-dimensional structure based on active Lamb waves", Smart Struct. Syst., Int. J., 2(2), 171-188. https://doi.org/10.12989/sss.2006.2.2.171   DOI
42 Li, W., Chen, B. and Cho, Y. (2020), "Nonlinear feature of phase matched Lamb waves in solid plate", Appl. Acoust., 160, 107124. https://doi.org/10.1016/j.apacoust.2019.107124   DOI
43 Singh, A.K., Tan, V.B., Tay, T.E. and Lee, H.P. (2019), "Experimental investigations into nonlinear vibro-acoustics for detection of delaminations in a composite laminate", J. Nondestruct. Eval. Diagn. Progn. Eng. Syst., 2(1), 011002. https://doi.org/10.1115/1.4041122   DOI
44 Cantrell, J.H. (2003), Fundamentals and Applications of Nonlinear Ultrasonic Nondestructive Evaluation, CRC Press.
45 Chen, Z., Tang, G., Zhao, Y., Jacobs, J.L. and Qu, J. (2014), "Mixing of collinear plane wave pulses in elastic solids with quadratic nonlinearity", J. Acoust. Soc. Am, 136, 2389-2404. https://doi.org/10.1121/1.4896567   DOI
46 Dao, P.B., Klepka, A., Pieczonka, L., Aymerich, F. and Staszewski, W.J. (2017), "Impact damage detection in smart composites using nonlinear acoustics-cointegration analysis for removal of undesired load effect", Smart Mater. Struct., 26(3), 0350. https://doi.org/10.1088/1361-665X/aa5744   DOI
47 Demcenko, A., Akkerman, R., Nagy, P.B. and Loendersloot, R. (2012), "Non-collinear wave mixing for non-linear ultrasonic detection of physical ageing in PVC", NDT & E Int., 49, 34-39. https://doi.org/10.1016/j.ndteint.2012.03.005   DOI
48 Ding, X., Zhao, Y., Hu, N., Liu, Y., Zhang, J. and Deng, M. (2018), "Experimental and numerical study of nonlinear Lamb waves of a low-frequency S0 mode in plates with quadratic nonlinearity", Materials, 11(11), 2096. https://doi.org/10.3390/ma11112096   DOI
49 Fierro, G.P.M. and Meo, M. (2015), "Residual fatigue life estimation using a nonlinear ultrasound modulation method", Smart Mater. Struct., 24(2), p. 025040. https://doi.org/10.1088/0964-1726/24/2/025040   DOI
50 Aslam, M., Bijudas, C.R., Nagarajan, P. and Remanan, M. (2020), "Numerical and Experimental Investigation of Nonlinear Lamb Wave Mixing at Low Frequency", J. Aerosp. Eng., 33(4), p. 04020037. https://doi.org/10.1061/(ASCE)AS.1943-5525.0001146   DOI