• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.04a
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• pp.722-725
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• 2014

The spatial focusing of time reversal Lamb waves on a plate has attracted considerable attention for identifying the location of an input source. This study investigates the spatial focusing performance on a plate with respect to the number of piezoelectric (PZT) sensors for varying locations of input sources. In particular, a small number of PZT sensors produce spatial focusing through the virtual sensor effect due to reflection of Lamb waves at plate edges. The spatial focusing performance with respect to the number of PZT sensors is quantified in terms of signal to noise ratio through numerical simulation and its implication is discussed.

• Structural Engineering and Mechanics
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• v.58 no.2
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• pp.347-378
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• 2016

Within the scope of the plane-strain state, by utilizing the three-dimensional linearized theory of elastic waves in initially stressed piezoelectric and elastic materials, Lamb wave propagation and the influence of the initial stresses on this propagation in a sandwich plate with pre-stressed piezoelectric face and pre-stressed metal elastic core layers are investigated. Dispersion equations are derived for the extensional and flexural Lamb waves and, as a result of numerical solution to these equations, the corresponding dispersion curves for the first (fundamental) and second modes are constructed. Concrete numerical results are obtained for the cases where the face layers' materials are PZT-2 or PZT-6B, but the material of the middle layer is Steel (St) or Aluminum (Al). Sandwich plates PZT-2/St/PZT-2, PZT-2/Al/PZT-2, PZT-6B/St/PZT-6B and PZT-6B/Al/PZT-6B are examined and the influence of the problem parameters such as piezoelectric and dielectric constants, layer thickness ratios and third order elastic constants of the St and Al on the effects of the initial stresses on the wave propagation velocity is studied.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.10a
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• pp.272-277
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• 2004

The elastic waves in the plate are dispersive waves with the characteristics of Lamb waves. However, $S_0$ symmetric mode is less dispersive in the frequency region less than first cut-off frequency. And, in anisotropic plates such as CFRP plates, the propagation velocities vary with the direction. So, the wave vector direction to be the phase velocity direction is not accord with the energy flow direction to be the group velocity direction. In this work, the group velocities of the $S_0$ symmetric mode less than the first cut-off frequency was analyzed with the group velocity dispersion curves in unidirectional CFRP plate. And, the group velocity curve obtained by the group velocity dispersion curves are compared with the measured velocities as varied the propagation direction of the Lamb wave. The measured velocities are good agreement with the corrected group velocity curve except near the fiber direction which is called the cusp region. When the propagation direction is not accorded with the principal axis, the direction of the group velocities declines to the fiber direction in the unidirectional CFRP plates. This implies that the energy propagates preferentially toward fiber direction.

• The Journal of the Acoustical Society of Korea
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• v.42 no.6
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• pp.559-564
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• 2023

It is known that change in the bone strength of cortical bone constituting the outer shell of long bones such as the tibia or radius due to aging and osteoporosis is a risk factor for fracture. In this study, the group velocity of time-reversed Lamb waves generated in tibial cortical bone in vivo was measured using a time reversal method, and the correlations of the group velocity with the cortical bone thickness (cTh) and cortical bone mineral density (cBMD) closely related to the bone strength were investigated. It was found that the group velocity of time-reversed Lamb waves measured in the right tibia of 7 subjects showed a very high correlation, r = 0.90 (p < 0.0001), with the cTh and a relatively low correlation, r = 0.69 (p < 0.0001), with the cBMD. A limitation of this in vivo study is that the group velocity of time-reversed Lamb waves was measured for a normal group consisting of only 7 healthy adults. In the future, if the clinical usefulness of the time-reversed Lamb wave is demonstrated by follow-up studies on normal and osteoporotic groups consisting of a large number of healthy adults and osteoporotic patients, respectively, it is expected to improve the reliability of quantitative ultrasound technology for osteoporosis diagnosis. In addition, it is necessary to expand the skeletal site for measuring the group velocity of time-reversed Lamb waves not only to the tibia but also to the femur or radius.

• Proceedings of the KSR Conference
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• 2008.06a
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• pp.2066-2072
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• 2008

The time reversal was investigated for direct root between PZT and PZT, but in case of a circular PZT, lamb wave moves not only along the direct root but also another roots. The center frequency of lamb wave is kept when the lamb waves are reflected from damage. This paper presents experimental and theoretical results for the new structural health monitoring method by above features of lamb wave, and we can increase accuracy of the new structural health monitoring method by using STFT(Short Time Fourier Transform).

• Advances in nano research
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• v.14 no.5
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• pp.463-474
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• 2023

The purpose of this paper is to present the analysis of propagating and evanescent waves in functionally graded (FG) nanoplates with the consideration of nonlocal effect. The analytical integration nonlocal stress expansion Legendre polynomial method is proposed to obtain complete dispersion curves in the complex domain. Unlike the traditional Legendre polynomial method that expanded the displacement, the presented polynomial method avoids employing the relationship between local stress and nonlocal stress to construct boundary conditions. In addition, the analytical expressions of numerical integrations are presented to improve the computational efficiency. The nonlocal effect, inhomogeneity of medium and their interactions on wave propagation are studied. It is found that the nonlocal effect and inhomogeneity of medium reduce the frequency bandwidth of complex evanescent Lamb waves, and make complex evanescent Lamb waves have a higher phase velocity at low attenuation. The occurrence of intersections of propagating Lamb wave in the nonlocal homogeneous plate needs to satisfy a smaller Poisson's ratio condition than that in the classical elastic theory. In addition, the inhomogeneity of medium enhances the nonlocal effect. The conclusions obtained can be applied to the design and dynamic response evaluation of composite nanostructures.

• Earthquakes and Structures
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• v.8 no.4
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• pp.821-841
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• 2015

This paper proposes a two-stage imaging approach for quantitative inspection of damages in metallic plates using the fundamental anti-symmetric mode of ($A_0$) Lamb wave. The proposed approach employs a number of transducers to transmit and receive $A_0$ Lamb wave pulses, and hence, to sequentially scan the plate structures before and after the presence of damage. The approach is applied to image the corrosion damages, which are simplified as a reduction of plate thickness in this study. In stage-one of the proposed approach a damage location image is reconstructed by analyzing the cross-correlation of the wavelet coefficient calculated from the excitation pulse and scattered wave signals for each transducer pairs to determine the damage location. In stage-two the Lamb wave diffraction tomography is then used to reconstruct a thickness reduction image for evaluating the size and depth of the damage. Finite element simulations are carried out to provide a comprehensive verification of the proposed imaging approach. A number of numerical case studies considering a circular transducer network with eight transducers are used to identify the damages with different locations, sizes and thicknesses. The results show that the proposed methodology is able to accurately identify the damage locations with inaccuracy of the order of few millimeters of a circular inspection area of $100mm^2$ and provide a reasonable estimation of the size and depth of the damages.

• Smart Structures and Systems
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• v.15 no.6
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• pp.1463-1479
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• 2015

Lamb waves have been a promising candidate for quantitative damage identification for various engineering structures, taking advantage of their superb capabilities of traveling for long distances with fast propagation and low attenuation. However, the application of Lamb waves in damage identification so far has been hampered by the fact that the characteristic signals associated with defects are generally weaker compared with those arising from boundary reflections, mode conversions and environmental noises, making it a tough task to achieve satisfactory damage identification from the time series. With awareness of this challenge, this paper proposes a time reversal-based technique to enhance the strength of damage-scattered signals, which has been previously applied to bulk wave-based damage detection successfully. The investigation includes (i) an analysis of Lamb wave propagation in a plate, generated by PZT patches mounted on the structure; (ii) an introduction of the time reversal theory dedicated for waveform reconstruction with a narrow-band input; (iii) a process of enhancing damage-scattered signals based on time reversal focalization; and (iv) the experimental investigation of the proposed approach to enhance the damage identification on a composite plate. The results have demonstrated that signals scattered by delamination in the composite plate can be enhanced remarkably with the assistance of the proposed process, benefiting from which the damage in the plate is identified with ease and high precision.

• The Journal of the Acoustical Society of Korea
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• v.25 no.3
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• pp.107-112
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• 2006

The elastic waves in a plate are dispersive waves due to the characteristics of Lamb waves. However, S0 symmetric mode is less dispersive in the frequency region below the first cut-off frequency. The wave Propagation velocities vary with the direction in anisotropic plates such as Carbon Fiber Reinforced Plastic (CFRP) Plates. The wave vector direction and energy flow vector direction are same in isotropic plates. However, the wave vector direction same as the phase velocity direction is not in accordance with the energy flow direction same as the group velocity direction in anisotropic plates. In this study. the dispersion curves or the phase velocity from anti-symmetric and symmetric Lamb wave dispersion equation are calculated for unidirectional laminated composite plate. Slowness surface is sketched using phase velocity under the first cut-off frequency. The direction and magnitude of group velocity are corrected with this slowness surface. The measured group velocities are in good agreement with the corrected group velocity curve except near the fiber direction zone which is called the cusp region.

• Structural Monitoring and Maintenance
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• v.4 no.4
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• pp.381-396
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• 2017

Structural health monitoring (SHM) is a necessity for reliable and efficient functioning of engineering systems. Damage detection (DD) is a crucial component of any SHM system. Lamb waves are a popular means to DD owing to their sensitivity to small damages over a substantial length. This typically involves an active sensing paradigm in a pitch-catch setting, that involves two piezo-sensors, a transmitter and a receiver. In this paper, we propose a data-intensive DD approach for beam structures using high frequency signals acquired from beams in a pitch-catch setting. The key idea is to develop a statistical learning-based approach, that harnesses the inherent sparsity in the problem. The proposed approach performs damage detection, localization in beams. In addition, quantification is possible too with prior calibration. We demonstrate numerically that the proposed approach achieves 100% accuracy in detection and localization even with a signal to noise ratio of 25 dB.