Lamb Waves In Thin Plates Research Articles

Analytical prediction of temperature effects on Lamb wave response in smart plates and its experimental verification

Abstract This article examines the effectiveness of a recently developed theoretical model for the generation and sensing of Lamb waves in thin plates with surface-bonded piezoelectric transducers in predicting temperature effects on Lamb waves and their time reversibility. In particular, the analytical model provides a closed-form solution, which incorporates both the shear-lag effect of the bonding layer and the system inertia in transducer-plate interaction modeling. Temperature-dependent material properties and thermal expansion of the system constituents are considered to predict the Lamb wave signal under a thermal environment. The accuracy of the theoretical prediction is assessed in comparison with experimental results obtained using an aluminum plate with adhesively bonded lead zirconate titanate transducers to its surface at different system temperatures ranging from 20°C to 75°C. Comparison is also made with experimental data and analytical solutions presented earlier without considering the inertia effect. The study reveals that the current solution accurately predicts the change in Lamb wave signal due to temperature variation, including the frequency dependency of the peak amplitude change with temperature rise. However, the theoretical model fails to predict the experimental trends when the inertia terms are neglected. The current model is also used to study the contributions of individual system parameters to the overall temperature effect on the time reversibility of Lamb waves and its dependence on the excitation frequency.

Hybrid experimental/computational approach to Time Reversal source localization in thin plates using image source method

Standard approaches to source localization usually rely on trilateration, using signals detected at multiple receiving points, with further research focused on improving localization robustness and reducing the number of sensors required. Time Reversal (TR) is a valid alternative, however it is often difficult to define a reliable hybrid (computational/experimental) approach, particularly in the case of plates where dispersive properties of the propagating waves play a crucial role to obtain focusing. In this paper, we present an analytical method that describes wave propagation in thin plates, accounting for edge reflections and dispersive properties, and validate it by comparison to experimental data. The Image Source Method (ISM), employed and extended in this study, provides an analytical means of Green's function computation through multiple edge-reflected propagation paths and proves to be reliable and fast to study propagation of Lamb waves in thin plates. A one-channel hybrid TR approach based on ISM is also proposed, utilizing experimental signals transferred to the model for backpropagation computation. In particular, the determination of the optimal signal duration to be time-reversed is discussed.

Lamb Wave Propagation Control Based on Modified GSL

As a new kind of elastic materials, elastic wave metasurface has great research significance in the field of elastic wave regulation. However, most of the researches on elastic wave metasurface are guided by traditional Generalized Snell’s Law (GSL), and the effect of higher order diffraction waves caused by structural periodicity is not considered. Under the action of higher order diffraction wave, the incident wave will produce more complex transmission phenomenon when passing through the metasurface, and the angle of transmission does not conform to GSL in some cases. In order to verify whether the modified GSL theory considering the higher-order diffraction term is still applicable to the regulation of solid elastic waves, this paper designs a helical metasurface based on the elastic wave theory of plate-beam structure, which is composed of helical lines of different lengths, and uses this structure to explain the complex transmission phenomenon of elastic wave metasurface. Finally, the asymmetric transmission, modal separation and waveguide of Lamb waves in thin plates are realized by combining the theory with structural design, which proves that the structure has great application potential in ultrasonic detection and other fields.

Role of transducer inertia in generation, sensing, and time-reversal process of Lamb waves in thin plates with surface-bonded piezoelectric transducers

An analytical model is presented for the generation, sensing, and time-reversible process of Lamb waves in thin isotropic plates with surface-bonded piezoelectric wafer transducers, incorporating the shear-lag effect of the bonding layer and inertia effects of the system in transducer modeling. A one-dimensional dynamic shear-lag model for the actuator-plate interaction is used to obtain the shear stress distribution at the actuator-plate interface. The Lamb wave solution for the plate under this shear traction excitation is obtained using the two-dimensional (2D) elasticity equations. A consistent sensor-plate interaction model incorporating the shear-lag and inertia effects is developed to determine the induced sensor voltage from the Lamb strain at the plate surface. The model is validated by comparing it with the 2D coupled piezoelasticity-based finite element simulation and experimental data. Detailed parametric studies are conducted to illustrate the effect of inclusion of inertia of actuator, sensor, adhesive, and plate in the transducer modeling on the Lamb wave generation, sensing, time reversibility, and the system’s best reconstruction frequency, and to ascertain how various geometrical and material parameters of the system influence the same. The developed closed-form solution will be immensely useful for the design of Lamb wave based structural health monitoring systems.

Time reversibility of Lamb waves in thin plates with surface-bonded piezoelectric transducers is temperature invariant at the best reconstruction frequency

The Lamb wave time-reversal method has been widely proposed as a baseline-free method for damage detection in thin-walled structures. Under varying thermal environments, it would require that the time reversibility of Lamb waves is temperature invariant. In this study, we examine the temperature dependence of Lamb waves and its time reversibility using experiments and finite element simulations on isotropic plates with surface-bonded piezoelectric wafer transducers for actuation and sensing. The study is conducted at three different temperatures of the system from 25°C to 75°C for a wide range of excitation frequency. The results indicate that the time reversibility can undergo significant changes due to temperature variations depending on the excitation frequency. However, at the best reconstruction frequency corresponding to the maximum similarity of the reconstructed signal with the original input signal (proposed recently as the probing frequency), the change in the percent similarity with temperature is insignificant. The results also demonstrate that changes in the physical properties of both adhesive layers and piezoelectric transducers with temperature play a dominant role in influencing Lamb wave amplitudes. However, only the change in the characteristics of the adhesive layers is responsible for the temperature dependence of the time reversibility of Lamb waves.

The Rapid Detection Technology of Lamb Wave for Microcracks in Thin-Walled Tubes

Thin-walled tubes are a kind of pressure vessel formed by a stamping and drawing process, which must withstand a great deal of sudden pressure during use. When microcrack defects of a certain depth are present on its inner and outer surfaces, severe safety accidents may occur, such as cracking and crushing. Therefore, it is necessary to carry out nondestructive testing of thin-walled tubes in the production process to eliminate the potential safety hazards. To realize the rapid detection of microcracks in thin-walled tubes, this study could be summarized as follows: (i) Because the diameters of the thin-walled tubes were much larger than their thicknesses, Lamb wave characteristics of plates with equal thicknesses were used to approximate the dispersion characteristics of thin-walled tubes. (ii) To study the dispersion characteristics of Lamb waves in thin plates, the detection method of the mode was determined using the particle displacement–amplitude curve. (iii) Using a multi-channel parallel detection method, rapid detection equipment for Lamb wave microcracks in thin-walled tubes was developed. (iv) The filtering peak values for defect signal detection with different depths showed that the defect detection peak values could reflect the defect depth information. (v) According to the minimum defect standard of a 0.045-mm depth, 100,000 thin-walled tubes were tested. The results showed that the missed detection rate was 0%, the reject rate was 0.3%, and the detection speed was 5.8 s/piece, which fully meets the actual detection requirements of production lines. Therefore, this study not only solved the practical issues for the rapid detection of microcracks in thin-walled tubes but also provided a reference for the application of ultrasonic technology for the detection of other components.

Mixing of ultrasonic Lamb waves in thin plates with quadratic nonlinearity

This paper investigates the propagation of Lamb waves in thin plates with quadratic nonlinearity by one-way mixing method using numerical simulations. It is shown that an A0-mode wave can be generated by a pair of S0 and A0 mode waves only when mixing condition is satisfied, and mixing wave signals are capable of locating the damage zone. Additionally, it is manifested that the acoustic nonlinear parameter increases linearly with quadratic nonlinearity but monotonously with the size of mixing zone. Furthermore, because of frequency deviation, the waveform of the mixing wave changes significantly from a regular diamond shape to toneburst trains.

Generation mechanism of nonlinear ultrasonic Lamb waves in thin plates with randomly distributed micro-cracks

Since the identification of micro-cracks in engineering materials is very valuable in understanding the initial and slight changes in mechanical properties of materials under complex working environments, numerical simulations on the propagation of the low frequency S0 Lamb wave in thin plates with randomly distributed micro-cracks were performed to study the behavior of nonlinear Lamb waves. The results showed that while the influence of the randomly distributed micro-cracks on the phase velocity of the low frequency S0 fundamental waves could be neglected, significant ultrasonic nonlinear effects caused by the randomly distributed micro-cracks was discovered, which mainly presented as a second harmonic generation. By using a Monte Carlo simulation method, we found that the acoustic nonlinear parameter increased linearly with the micro-crack density and the size of micro-crack zone, and it was also related to the excitation frequency and friction coefficient of the micro-crack surfaces. In addition, it was found that the nonlinear effect of waves reflected by the micro-cracks was more noticeable than that of the transmitted waves. This study theoretically reveals that the low frequency S0 mode of Lamb waves can be used as the fundamental waves to quantitatively identify micro-cracks in thin plates.

Phononic plate waves

In the past two decades, phononic crystals (PCs) which consist of periodically arranged media have attracted considerable interest because of the existence of complete frequency band gaps and maneuverable band structures. Recently, Lamb waves in thin plates with PC structures have started to receive increasing attention for their potential applications in filters, resonators, and waveguides. This paper presents a review of recent works related to phononic plate waves which have recently been published by the authors and coworkers. Theoretical and experimental studies of Lamb waves in 2-D PC plate structures are covered. On the theoretical side, analyses of Lamb waves in 2-D PC plates using the plane wave expansion (PWE) method, finite-difference time-domain (FDTD) method, and finite-element (FE) method are addressed. These methods were applied to study the complete band gaps of Lamb waves, characteristics of the propagating and localized wave modes, and behavior of anomalous refraction, called negative refraction, in the PC plates. The theoretical analyses demonstrated the effects of PC-based negative refraction, lens, waveguides, and resonant cavities. We also discuss the influences of geometrical parameters on the guiding and resonance efficiency and on the frequencies of waveguide and cavity modes. On the experimental side, the design and fabrication of a silicon-based Lamb wave resonator which utilizes PC plates as reflective gratings to form the resonant cavity are discussed. The measured results showed significant improvement of the insertion losses and quality factors of the resonators when the PCs were applied.

Detection of Suspicious Mass on Structures by Acoustical Waves

Analysis of scattered Lamb waves in thin plates and shells, with an added foreign mass on their surface, was performed. Waves were generated in a range of frequencies, up to 80 kHz, by an impact loading. The responses were detected by full-field and point-wise optical methods. Pulse holointerferometry and pulse electronic speckle patterns interferometry techniques were used to visualize the interaction of the Lamb waves with the added foreign mass. Double-channel laser vibrometry was used to record the velocity history within the proximity of the added foreign mass. It was shown that frequency analysis of the recorded waveforms was more convenient than time domain analysis when investigating the response in the thin-walled structures. The proposed method is applicable to search for suspicious masses (e.g. explosive devices) added to the structures.

Band gaps of lower-order Lamb wave in thin plate with one-dimensional phononic crystal layer: Effect of substrate

We study the substrate effect on the band gaps of lower-order Lamb waves propagating in thin plate with one-dimensional phononic crystal layer coated on uniform substrate. The transmitted power spectra are calculated by using the finite element method (FEM). The results show that when the substrate is hard, the influences on band gap are significant and the band gaps disappear rapidly as the substrate becomes thicker. However, when the substrate is soft, the depth of band gaps becomes larger as the thickness of the substrate increases. A virtual plane wave expansion method is developed to calculate the dispersion curves of Lamb wave. The locations and widths of band gaps on the dispersion curves are in good agreement with the results from the transmitted power spectra by FEM.

A tilted angle polarization type piezoelectric transducer for plate wave generation

A tilted angle polarization type piezoelectric transducer (TAPP) is newly suggested to generate the Lamb waves in thin plate without wedge. The tilted angle between the TAPP and the aluminum plate is easily determined by Snell's law. Our new type TAPP with a tilted angle of 50° for S0 mode Lamb wave generation was specially manufactured. Preliminary experiments have been performed to examine the usefulness of our TAPP. As a result, efficient radiation of S0 mode Lamb wave from TAPP was confirmed and was clearly identified by the wavelet transform analysis.

Laser-based ultrasonic generation and detection of zero-group velocity Lamb waves in thin plates

A novel laser-based ultrasonic technique for the inspection of thin plates and membranes is presented, in which a modulated continuous-wave laser source is used to excite narrow bandwidth Lamb waves. The dominant feature in the acoustic spectrum is a sharp resonance peak that occurs at the minimum frequency of the first-order symmetric Lamb mode, where the group velocity of the Lamb wave goes to zero while the phase velocity remains finite. Experimental results with the laser source and receiver on epicenter demonstrate that the zero-group velocity resonance generated with a low-power modulated excitation source can be detected using a Michelson interferometer coupled to a lock-in amplifier. This resonance peak is sensitive to the thickness and mechanical properties of plates and may be suitable, for example, for the measurement and mapping of nanoscale thickness variations.

Normal mode expansion method for laser-generated ultrasonic Lamb waves in orthotropic thin plates

A quantitative theory for modeling the laser-generated transient ultrasonic Lamb waves, which propagates along arbitrary directions in orthotropic plates, is presented by employing an expansion method of generalized Lamb wave modes. The displacement field is expressed by a summation of the symmetric and antisymmetric modes in the surface stress-free orthotropic plate, and therefore the theory is particularly appropriate for waveform analyses of Lamb waves in thin plates because one needs only to evaluate several lower modes. The transient waveforms excited by the thermoelastic expansion and the oil-coating evaporation are analyzed for a transversely isotropic thin plate. The results show that the theory provides a quantitative analysis to characterize anisotropic elastic stiffness properties of orthotropic plates by laser-generated Lamb wave detection.

Quantitative theory for laser-generated Lamb waves in orthotropic thin plates

A quantitative theory for modeling the laser-generated transient ultrasonic Lamb waves propagating along arbitrary directions in orthotropic thin plates is presented by employing an expansion method of the generalized Lamb wave modes. The displacement is expressed by a summation of the symmetric and antisymmetric modes in the surface stress-free orthotropic plate, and it is particularly appropriate for wave form analyses of Lamb wave in thin plates because one needs only to evaluate a few of the lowest order modes. The transient wave forms are analyzed in the thermoelastic regime and the oil coating generation method for a transversely isotropic plate. The results show that the theory provides a quantitative analysis to characterize anisotropic properties and elastic stiffness properties of the orthotropic plates by the laser-generated Lamb wave detection.

Excitations of thermoelastic waves in plates by a pulsed laser

The method of the eigenfunction expansion, also known as the expansion in normal modes, is employed to study numerically the axisymmetric excitation of the thermoelastic waves in plates by a pulsed laser. This method gives a systematic treatment and allows one to investigate not only the quasistatic and dynamic thermoelastic responses of pulsed photothermal deformation on the time scale of 1 μs, but also the thermoelastic generation of longitudinal, transverse, and surface acoustic waves in thick materials, as well as the excitations of the Rayleigh-Lamb wave modes in thin plates. The formalism is particularly suitable for waveform analyses of the excitations of transient Lamb waves in thin plates because one needs only to calculate the contributions of several lower eigenmodes. The numerical technique provides a quantitative tool for the experimental determination of material properties, especially the mechanical and elastic properties of free-standing films and thicker sheet materials by thermoelastic detection.

Air-coupled piezoelectric detection of laser-generated ultrasound

A pulsed laser has been used to generate ultrasonic transients in samples of metal and fiber-reinforced polymer composite material. These have been detected using an air-coupled piezoelectric transducer. It is demonstrated that such a transduction system can be used for longitudinal waves in bulk material, Rayleigh waves at solid surfaces and Lamb waves in thin plates.

Laser generation of antisymmetric lamb waves in thin plates

A convenient method is described for optically exciting and monitoring Lamb waves in thin plates. The interference pattern of two high power laser beams on a sample surface produces periodic heating and thus coherent antisymmetric Lamb waves are excited. By varying the interface fringe spacing, the acoustic frequency is easily and continuously tunable from 2.5 to 23 MHz with the present experimental apparatus. The ultrasound velocities as a function of frequency are measured to determine a dispersion curve, from which the Young's modulus is deduced. Furthermore, the temperature dependence is estimated from the velocity changes. Experimental results are presented for several kinds of brittle plate and thin film materials.