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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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Figures

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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