Research Papers

Asymmetric Lamb Wave Propagation and Mode Isolation in Thin Plate With Spatiotemporal Periodic Stiffness

[+] Author and Article Information
Liuxian Zhao

Temasek Laboratories,
Nanyang Technological University,
50 Nanyang Drive,
Singapore 637553
e-mail: lxzhao@ntu.edu.sg

Chang Quan Lai

Temasek Laboratories,
Nanyang Technological University,
50 Nanyang Drive,
Singapore 637553
e-mail: cqlai@ntu.edu.sg

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received October 17, 2018; final manuscript received April 2, 2019; published online May 22, 2019. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 141(5), 051005 (May 22, 2019) (6 pages) Paper No: VIB-18-1449; doi: 10.1115/1.4043509 History: Received October 17, 2018; Accepted April 04, 2019

The Lamb wave propagation through a thin plate with periodic spatiotemporal variation of material property was investigated through numerical simulations. It was found that regular oscillations of Young's modulus in both space and time can lead to the creation of distinct band gaps for different modes of Lamb wave. Moreover, the dispersion relation for each mode was dependent on the direction of wave propagation (i.e., nonreciprocal). These results allow the Lamb wave modes to be reduced to a single mode traveling in a single direction for specific frequencies. This frequency range was observed to widen with an increasing modulation amplitude of Young's modulus but was not significantly altered by the modulation frequency. The insights derived from this study indicate that spatiotemporal control of material property can be used to effectively isolate Lamb wave modes and reduce reflections, leading to an improvement in the accuracy of the structural health monitoring of materials.

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Filho, J. F. M. R., Tremblay, N., Fonseca, G. S., and Belanger, P., 2017, “The Feasibility of Structural Health Monitoring Using the Fundamental Shear Horizontal Guided Wave in a Thin Aluminum Plate,” Materials, 10(5), pp. 551–560. [CrossRef]
Giurgiutiu, V., 2005, “Tuned Lamb Wave Excitation and Detection With Piezoelectric Wafer Active Sensors for Structural Health Monitoring,” J. Intell. Mater. Syst. Struct., 16(4), pp. 291–305. [CrossRef]
Ong, W. H., and Chiu, W. K., 2013, “Designing for Lamb Wave Based In-Situ Structural Health Monitoring,” Key Eng. Mater., 558, pp. 411–423. [CrossRef]
Santoni, G. B., Yu, L., and Giurgiutiu, V., 2007, “Lamb Wave-Mode Tuning of Piezoelectric Wafer Active Sensors for Structural Health Monitoring,” Trans. ASME J. Vib. Acoust., 129(6), pp. 752–762. [CrossRef]
Park, I., Jun, Y., and Lee, U., 2014, “Lamb Wave Mode Decomposition for Structural Health Monitoring,” Wave Motion, 51(2), pp. 335–347. [CrossRef]
Ostachowicz, W., and Radzienski, M., 2012, Structural Health Monitoring by Means of Elastic Wave Propagation in Modern Practice in Stress and Vibration Analysis 2012 (MPSVA 2012), 28-31, IOP Publishing Ltd, UK.
Mitra, M., and Gopalakrishnan, S., 2016, “Guided Wave Based Structural Health Monitoring: A Review,” Smart Mater. Struct., 25(5), p. 053001. [CrossRef]
Schubert, K. J., Brauner, C., and Herrmann, A. S., 2014, “Non-Damage-Related Influences on Lamb Wave-Based Structural Health Monitoring of Carbon Fiber-Reinforced Plastic Structures,” Struct. Health Monit., 13(2), pp. 158–176. [CrossRef]
Wu, T. T., Wu, Z., Huang, G., and Lin, S., 2004, “Surface and Bulk Acoustic Waves in Two-Dimensional Phononic Crystal Consisting of Materials With General Anisotropy,” Phys. Rev. B Condens. Matter Mater. Phys. 69(9), p. 94301. [CrossRef]
Deymier, P. A., 2013, Acoustic Metamaterials and Phononic Crystals, Springer, Berlin, New York.
Huang, G. L., and Sun, C. T., 2010, “Band Gaps in a Multiresonator Acoustic Metamaterial,” ASME J. Vib. Acoust., 132(3), p. 031003. [CrossRef]
Akozbek, N., Mattiucci, N., Bloemer, M. J., Sanghadasa, M., and D'Aguanno, G., 2014, “Manipulating the Extraordinary Acoustic Transmission Through Metamaterial-Based Acoustic Band Gap Structures,” Appl. Phys. Lett., 104(16), pp. 161906. [CrossRef]
Hou, Z., and Assouar, B. M., 2008, “Modeling of Lamb Wave Propagation in Plate With Two-Dimensional Phononic Crystal Layer Coated on Uniform Substrate Using Plane-Wave-Expansion Method,” Phys. Lett. A, 372(12), pp. 2091–2097. [CrossRef]
Zhao, M., Xie, Y., Zhang, X., and Gao, J., 2013, “Band Gaps of Lamb Waves Propagating in One-Dimensional Periodic and Nesting Fibonacci Superlattices Thin Plates,” Thin Solid Films, 546, pp. 439–442. [CrossRef]
Chen, J.-J., and Han, X., 2010, “The Propagation of Lamb Waves in One-Dimensional Phononic Crystal Plates Bordered With Symmetric Uniform Layers,” Phys. Lett. A, 374(31–32), pp. 3243–3246. [CrossRef]
Yao, Y., Wu, F., Zhang, X., and Hou, Z., 2011,” J. Appl. Phys., 110(12), p. 123503. [CrossRef]
Zhu, X. F., Liu, S., Xu, T., Wang, T., and Cheng, J., 2010, “Investigation of a Silicon-Based One-Dimensional Phononic Crystal Plate via the Super-Cell Plane Wave Expansion Method,” Chin. Phys. B, 19(4), p. 044301. [CrossRef]
Chen, J. J., Yan, F., and Chan, H., 2008, “Large Lamb Wave Band Gap in Phononic Crystals Thin Plates,” Appl. Phys. B: Lasers Opt., 90(3–4), pp. 557–559. [CrossRef]
Hou, Z., and Assouar, B. M., 2009, “Numerical Investigation of the Propagation of Elastic Wave Modes in a One-Dimensional Phononic Crystal Plate Coated on a Uniform Substrate,” J. Phys. D: Appl. Phys., 42(8), p. 085103. [CrossRef]
Sun, J. H., Lan, C., Kuo, C., and Wu, T. T., 2012, “A ZnO/Silicon Lamb Wave Filter Using Phononic Crystals,” 2012 IEEE International Frequency Control Symposium (FCS), Piscataway, NJ, May 21–24.
Serhane, R., Hadj-Larbi, F., Hassein-Bey, A., and Khelif, A., 2018, “Selective Band Gap to Suppress the Spurious Acoustic Mode in Film Bulk Acoustic Resonator Structures,” ASME J. Vib. Acoust., 140(3), p. 031018. [CrossRef]
Maznev, A. A., Every, A. G., and Wright, O. B., 2013, “Reciprocity in Reflection and Transmission: What is a ‘Phonon Diode?,” Wave Motion, 50(4), pp. 776–784. [CrossRef]
Chen, J. J., Han, X., and Li, G. Y., 2013, “Asymmetric Lamb Wave Propagation in Phononic Crystal Slabs With Graded Grating,” J. Appl. Phys., 113(18), p. 184506. [CrossRef]
Li, J., and Chen, J. J., 2016, “Unidirectional and Tunable Acoustic Diode Made by Asymmetric Double Layer Metallic Grating With Periodical Structure,” 2016 Symposium on Piezoelectricity, Acoustic Waves and Device Applications (SPAWDA), Piscataway, NJ, Oct. 21–24.
Chaunsali, R., Li, F., and Yang, F., 2016, “Stress Wave Isolation by Purely Mechanical Topological Phononic Crystals,” Sci. Rep., 6, p. 30662. [CrossRef] [PubMed]
Wang, P., Lu, L., and Bertoldi, K., 2015, “Topological Phononic Crystals With One-Way Elastic Edge Waves,” Phys. Rev. Lett., 115(10), p. 104302. [CrossRef] [PubMed]
Croenne, C., Vasseur, J. O., Bou Matar, O., Ponge, M. F., Deymier, P. A., Hladky-Hennion, A. C., and Dubus, B., 2017, “Brillouin Scattering-Like Effect and Non-Reciprocal Propagation of Elastic Waves due to Spatio-Temporal Modulation of Electrical Boundary Conditions in Piezoelectric Media,” Appl. Phys. Lett., 110(6), p. 061901. [CrossRef]
Swinteck, N., Matsuo, S., Runge, K., Vasseur, J. O., Lucas, P., and Deymier, P. A., 2015, “Bulk Elastic Waves With Unidirectional Backscattering-Immune Topological States in a Time-Dependent Superlattice,” J. Appl. Phys., 118(6), p. 063103. [CrossRef]
Trainiti, G., and Ruzzene, M., 2016, “Non-Reciprocal Elastic Wave Propagation in Spatiotemporal Periodic Structures,” New J. Phys., 18(8), p. 083047. [CrossRef]
Attarzadeh, M. A., and Nouh, M., 2018, “Elastic Wave Propagation in Moving Phononic Crystals and Correlations With Stationary Spatiotemporally Modulated Systems,” AIP Adv., 8(10), p. 105302. [CrossRef]
Ansari, M. H., Attarzadeh, M. A., Nouh, M., and Karami, M. A., 2018, “Application of Magnetoelastic Materials in Spatiotemporally Modulated Phononic Crystals for Nonreciprocal Wave Propagation,” Smart Mater. Struct., 27(1), p. 015030. [CrossRef]
Popa, B. I., Zhai, Y., and Kwon, H., 2018, “Acoustic Bianisotropic Metasurfaces for Broadband Non-Reciprocal Sound Transport,” J. Acoust. Soc. Am., 144(3), pp. 1831–1831. [CrossRef]
Attarzadeh, M. A., Al Ba’ba’a, H., and Nouh, M., 2018, “On the Wave Dispersion and Non-Reciprocal Power Flow in Space-Time Traveling Acoustic Metamaterials,” Appl. Acoust., 133, pp. 210–214. [CrossRef]
Attarzadeh, M. A., and Nouh, M., 2018, “Non-Reciprocal Elastic Wave Propagation in 2D Phononic Membranes With Spatiotemporally Varying Material Properties,” J. Sound Vib., 422, pp. 264–277. [CrossRef]
Krokhin, A., Neogi, A., Walker, E., and Bozhko, A., 2018, “Non-reciprocal Acoustic Transmission Through a Dissipative Phononic Crystal with Asymmetric Scatterer,” Health Monitoring of Structural and Biological Systems XII, Denver, CO, Apr. 3.
Zanjani, M. B., Davoyan, A. R., Mahmoud, A. M., Engheta, N., and Lukes, J. R., 2014, “One-Way Phonon Isolation in Acoustic Waveguides,” Appl. Phys. Lett., 104(8), p. 081905. [CrossRef]
Wang, Y., Yousefzadeh, B., Chen, H., Nassar, H., Huang, G., and Daraio, C., 2018, “Observation of Nonreciprocal Wave Propagation in a Dynamic Phononic Lattice,” Phys. Rev. Lett., 121(19), p. 194301. [CrossRef] [PubMed]
Naizhi, Z., and Shi, Y., 2010, “Experimental Research on Damage Detection of Large Thin Aluminum Plate Based on Lamb Wave,” Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, San Diego, CA, Feb.
Giurgiutiu, V., 2008, Structural Health Monitoring With Piezoelectric Wafer Active Sensors, Academic Press, Cambridge, MA.
ANSYS, Inc. ansys 15.0, Help Electromagnetic Analysis Guide.
Semblat, J. F., Lenti, L., and Gandomzadeh, A., 2011, “A Simple Multi-Directional Absorbing Layer Method to Simulate Elastic Wave Propagation in Unbounded Domains,” Int. J. Numer. Methods Eng., 85(12), pp. 1543–1563. [CrossRef]
Kwok, K. W., Wang, B., Chan, H., and Choy, C. L., 2002, Self-Polarization in PZT Films, Taylor and Francis Inc., London.
Ruzzene, F. R. A. M., 2012, Wave Propagation in Linear and Nonlinear Periodic Media: Analysis and Applications, Springer, New York.
Van Belle, L., Deckers, E., Claeys, C., and Desmet, W., 2017, “Sound Transmission Loss of a Locally Resonant Metamaterial Using the Hybrid Wave Based—Finite Element Unit Cell Method,” 11th International Congress on Engineered Materials Platforms for Novel Wave Phenomena (Metamaterials), Piscataway, NJ, Aug. 27–Sept. 2.
Ang, L. Y. L., Koh, Y. K., and Lee, H. P., 2018, “Plate-Type Acoustic Metamaterial With Cavities Coupled via an Orifice for Enhanced Sound Transmission Loss,” Appl. Phys. Lett., 112(5), p. 051903. [CrossRef]
DeSalvo, G. J., and Swanson, J. A., 1985, “ANSYS Engineering Analysis System User's,” Swanson Analysis Systems.
Liu, W., and Giurgiutiu, V., 2007, “Finite Element Simulation of Piezoelectric Wafer Active Sensors for Structural Health Monitoring With Coupled-Filed Elements,” Nondestructive Evaluation and Health Monitoring, San Diego, CA, Apr. 10.
Yang, J., 2009, Special Topics in the Theory of Piezoelectricity, Springer, New York.
Song, F., Huang, G. L., Kim, J. H., and Haran, S., 2008, “On the Study of Surface Wave Propagation in Concrete Structures Using a Piezoelectric Actuator/Sensor System,” Smart Mater. Struct., 17(5), p. 055024. [CrossRef]
Zhao, L., Conlon, S. C., and Semperlotti, F., 2014, “Broadband Energy Harvesting Using Acoustic Black Hole Structural Tailoring,” Smart Mater. Struct., 23(6), p. 065021. [CrossRef]
Shen, Y., and Giurgiutiu, V., 2014, “Predictive Modeling of Nonlinear Wave Propagation for Structural Health Monitoring With Piezoelectric Wafer Active Sensors,” J. Intell. Mater. Syst. Struct., 25(4), pp. 506–520. [CrossRef]


Grahic Jump Location
Fig. 1

Periodic modulation of Young's modulus in both the space and time domains given by Eq. (1): (a) spatial-only modulation (ωm = 0 rad/s) and (b) spatiotemporal modulation (ωm = 5000π rad/s). The scale bar indicates the value of the Young's modulus.

Grahic Jump Location
Fig. 2

Numerical model for Lamb wave propagation in a thin plate: (a) schematic of a thin plate excited using PZT at the center location, a single PZT is used at the bottom of the plate to generate both symmetric and antisymmetric Lamb wave modes, (b) a wide band frequency sweep signal, and (c) its frequency spectrum using fast Fourier transform

Grahic Jump Location
Fig. 3

(a) Time–space plot and (b) frequency–wavenumber (fk) plot for the constant plate. (c) Time–space plot and (d) frequency–wavenumber (fk) plot of the spatial variation plate. (e) Time–space plot and (f) frequency–wavenumber (fk) plot of the spatiotemporal variation plate. (g) Magnified view of plot in (d). (h) Magnified view of plot in (f). A0 and S0 refer to the asymmetric Lamb mode and symmetric Lamb mode, respectively. The scale bar in the figures indicates the displacement in the thickness direction (mm).

Grahic Jump Location
Fig. 4

Time–space analysis of the spatiotemporal variation plate using central frequency f = 24 kHz: (a) time–space plot and (b) time–space plot at nine different locations. The scale bar in figure (a) indicates the displacement in the thickness direction (mm).

Grahic Jump Location
Fig. 5

Range of propagating wave frequency where the S0 mode cannot propagate and the A0 mode can only travel unidirectionally in the −x direction, with respect to variations in the (a) amplitude of Young's modulus modulation Em and (b) angular frequency of modulation ωm

Grahic Jump Location
Fig. 6

Two PZTs are used at the top and bottom of the plate to generate either symmetric or antisymmetric Lamb wave modes. Pure S0 Lamb wave mode can be generated by applying symmetric excitation signals onto both PZTs, while A0 Lamb wave mode can be generated by applying asymmetric excitation signals.

Grahic Jump Location
Fig. 7

Transmission analysis for constant plate, spatial variation plate and spatiotemporal variation plate at different propagation frequencies. Plots of frequency against TR of (a) S0 for constant plate, (b) S0 for spatial variation plate, (c) S0 for spatiotemporal variation plate, (d) A0 for constant plate, (e) A0 for spatial variation plate, and (f) A0 for spatiotemporal variation plate.



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