Showing papers on "Lamb waves published in 2007"

Fatigue crack detection in metallic structures with Lamb waves and 3D laser vibrometry

Abstract: The paper presents the application of ultrasonic guided waves for fatigue crack detection in metallic structures. The study involves a simple fatigue test performed to introduce a crack into an aluminium plate. Lamb waves generated by a low-profile, surface-bonded piezoceramic transducer are sensed using a tri-axis, multi-position scanning laser vibrometer. The results demonstrate the potential of laser vibrometry for simple, rapid and robust detection of fatigue cracks in metallic structures. The method could be used in quality inspection and in-service maintenance of metallic structures in aerospace, civil and mechanical engineering industries.

Single Mode Tuning Effects on Lamb Wave Time Reversal with Piezoelectric Wafer Active Sensors for Structural Health Monitoring

Abstract: Lamb wave time reversal method is a new and tempting baseline-free damage detection technique for structural health monitoring. With this method, certain types of damage can be detected without baseline data. However, the application of this method using piezoelectric wafer active sensors (PWAS) is complicated by the existence of at least two Lamb wave modes at any given frequency, and by the dispersion nature of the Lamb wave modes existing in thin-wall structures. The theory of PWAS-related Lamb wave time reversal has not yet been fully studied.

Vibrations and Waves in Continuous Mechanical Systems

Abstract: Preface . 1 Vibrations of strings and bars. 1.1 Dynamics of strings and bars: the Newtonian formulation. 1.2 Dynamics of strings and bars: the variational formulation. 1.3 Free vibration problem: Bernoulli's solution. 1.4 Modal analysis. 1.5 The initial value problem: solution using Laplace transform. 1.6 Forced vibration analysis. 1.7 Approximate methods for continuous systems. 1.8 Continuous systems with damping. 1.9 Non-homogeneous boundary conditions. 1.10 Dynamics of axially translating strings. Exercises. References. 2 One-dimensional wave equation: d'Alembert's solution. 2.1 D'Alembert's solution of the wave equation. 2.2 Harmonic waves and wave impedance. 2.3 Energetics of wave motion. 2.4 Scattering of waves. 2.5 Applications of the wave solution. Exercises. References. 3 Vibrations of beams. 3.1 Equation of motion. 3.2 Free vibration problem. 3.3 Forced vibration analysis. 3.4 Non-homogeneous boundary conditions. 3.5 Dispersion relation and flexural waves in a uniform beam. 3.6 The Timoshenko beam. 3.7 Damped vibration of beams. 3.8 Special problems in vibrations of beams. Exercises. References. 4 Vibrations of membranes. 4.1 Dynamics of a membrane. 4.2 Modal analysis. 4.3 Forced vibration analysis. 4.4 Applications: kettledrum and condenser microphone. 4.5 Waves in membranes. Exercises. References. 5 Vibrations of plates. 5.1 Dynamics of plates. 5.2 Vibrations of rectangular plates. 5.2.1 Free vibrations. 5.3 Vibrations of circular plates. 5.4 Waves in plates. 5.5 Plates with varying thickness. Exercises. References. 6 Boundary value and eigenvalue problems in vibrations. 6.1 Self-adjoint operators and eigenvalue problems for undamped free vibrations. 6.2 Forced vibrations. 6.3 Some discretization methods for free and forced vibrations. References. 7 Waves in fluids. 7.1 Acoustic waves in fluids. 7.2 Surface waves in incompressible liquids. Exercises. References. 8 Waves in elastic continua. 8.1 Equations of motion. 8.2 Plane elastic waves in unbounded continua. 8.3 Energetics of elastic waves. 8.4 Reflection of elastic waves. 8.5 Rayleigh surface waves. 8.6 Reflection and refraction of planar acoustic waves. Exercises. References. A The variational formulation of dynamics. References. B Harmonic waves and dispersion relation. B.1 Fourier representation and harmonic waves. B.2 Phase velocity and group velocity. References. C Variational formulation for dynamics of plates. References. Index.

Experimental characterization of material nonlinearity using Lamb waves

Abstract: The objective of this research is to develop an accurate and reliable procedure to measure the second order harmonic of a Lamb wave propagating in a metallic plate. There are two associated complications in measuring these nonlinear Lamb waves, namely, their inherent dispersive and multimode natures. To overcome these, this research combines a time-frequency representation with a hybrid wedge generation and laser interferometric detection system. The effectiveness of the proposed procedure is demonstrated by characterizing the inherent material nonlinearity of two different aluminum plates whose absolute nonlinearity parameters are known from longitudinal wave measurements.

Assessment of accumulated fatigue damage in solid plates using nonlinear Lamb wave approach

Abstract: The feasibility of using the nonlinear effect of primary Lamb wave propagation for assessing accumulated fatigue damage in solid plates is theoretically analyzed. After the aluminum sheets are subjected to tension-tension fatigue loading for different numbers of loading cycles, they are subjected to ultrasonic tests near the driving frequency where Lamb waves have a strong nonlinearity. This is followed by the measurement of the amplitude-frequency curves for second harmonics of the considered Lamb waves. The experimental results show that the effect of second-harmonic generation by Lamb wave propagation is very sensitive to the accumulation of fatigue damage of solid plates.

Lamb waves in binary locally resonant phononic plates with two-dimensional lattices

Abstract: The authors study the propagation of Lamb waves in two-dimensional locally resonant phononic-crystal plates, composed of periodic soft rubber fillers in epoxy host with a finite thickness. Our calculations are based on the efficient plane wave expansion formulation which utilized Mindlin’s plate theory. Calculated results show that the low-frequency gaps of Lamb waves are opened up by the localized resonance mechanism. The resonant frequencies of flexure-dominated plate modes are significantly dependent not only on the radius of circular rubber fillers but also on the plate thickness. The properties of localized resonance are qualitatively analogous to the vibration of a circular thin plate.

Foundations of Stress Waves

Abstract: Chapter 1. Introduction Chapter 2. Elementary Theory of One-Dimensional Stress Waves in Bars Chapter 3. Interaction of Elastic Longitudinal Waves Chapter 4. Interaction of Elastic-Plastic Longitudinal Waves in Bars Chapter 5. Rigid Unloading Approximation Chapter 6. One-Dimensional Visco-Elastic Waves and Elastic-Visco-Plastic Waves Chapter 7. One-Dimensional Strain Plane Waves Chapter 8. Spherical Waves and Cylindrical Waves Chapter 9. Elastic Plastic Waves Propagating in Flexible Strings Chapter 10. Elastic Plastic Waves Propagating in Beams under Transverse Impact (Bending Wave Theory) Chapter 11. General Theory for Linear Elastic Waves Chapter 12. Numerical Methods for Stress Wave Propagation

Damage Detection in Composite Plates by Using an Enhanced Time Reversal Method

Abstract: A damage detection technique, which does not rely on any past baseline signals, is proposed to assess damage in composite plates by using an enhanced time reversal method. A time reversal concept of modern acoustics has been adapted to guided-wave propagation to improve the detectability of local defects in composite structures. In particular, wavelet-based signal processing techniques have been developed to enhance the time reversibility of Lamb waves in thin composite laminates. In the enhanced time reversal method, an input signal at an excitation point can be reconstructed if a response signal measured at another point is reemitted to the original excitation point after being reversed in a time domain. This time reversibility is based on linear reciprocity of elastic waves, and it is violated when nonlinearity is caused by a defect along a direct wave path. Examining the deviation of the reconstructed signal from the known initial input signal allows instantaneous identification of damage without requiring the baseline signal for comparison. The validity of the proposed method has been exemplified through experimental studies on a quasi-isotropic laminate with delamination.

Evaluation of plasticity driven material damage using Lamb waves

Abstract: This letter reports on the experimental observation of a direct correlation between the acoustic nonlinearity measured with Lamb waves and the level of plasticity in a metal specimen. This correlation implies that even though Lamb waves are multimodal and dispersive, they will interact with a material’s plasticity in a manner similar to longitudinal and Rayleigh waves; there is a fundamental relationship between material plasticity and acoustic nonlinearity that is independent of wave type. As a result, Lamb waves can be used to quantitatively assess plasticity driven material damage using established higher harmonic generation techniques.

Instantaneous reference-free crack detection based on polarization characteristics of piezoelectric materials

Abstract: A new methodology of guided-wave-based nondestructive testing (NDT) is developed to detect crack damage in a thin metal structure without using prior baseline data or a predetermined decision boundary. In conventional guided-wave-based techniques, damage is often identified by comparing the 'current' data obtained from a potentially damaged condition of a structure with the 'past' baseline data collected at the pristine condition of the structure. However, it has been reported that this type of pattern comparison with the baseline data can lead to increased false alarms due to its susceptibility to varying operational and environmental conditions of the structure. To develop a more robust damage diagnosis technique, a new concept of NDT is conceived so that cracks can be detected even when the system being monitored is subjected to changing operational and environmental conditions. The proposed NDT technique utilizes the polarization characteristics of the piezoelectric wafers attached on both sides of the thin metal structure. Crack formation creates Lamb wave mode conversion due to a sudden change in the thickness of the structure. Then, the proposed technique instantly detects the appearance of the crack by extracting this mode conversion from the measured Lamb waves, and the threshold value from damage classification is also obtained only from the current dataset. Numerical and experimental results are presented to demonstrate the applicability of the proposed technique to instantaneous crack detection.

Structural Damage Location with Fiber Bragg Grating Rosettes and Lamb Waves

Abstract: The aim of this study is to present the results of testing a damage detection and damage localization system based on fiber Bragg grating sensors. The objective of the system is to detect and locate damage in structures such as those found in aerospace applications. The damage identification system involves Bragg gratings for sensing ultrasound by detecting the linear strain component produced by Lamb waves. A tuneable laser is used for the interrogation of the Bragg gratings to achieve high sensitivity detection of ultrasound. The interaction of Lamb waves with damage, e.g., the reflection of the waves at defects, allows the detection of damage in structures by monitoring the Lamb wave propagation characteristics. As the reflected waves produce additional components within the original signal, most of the information about the damage can be found in the differential signal of the reference and the damage signal. Making use of the directional properties of the Bragg grating the direction of the reflected acoustic waves can be determined by mounting three of the gratings in a rosette configuration. Two suitably spaced rosettes are used to locate the source of the reflection, i.e., the damage, by taking the intersection of the directions given by each rosette. A genetic algorithm (GA) can be used to calculate that intersection and to account for any ambiguities from the Lamb wave measurements. The performance of the GA has been studied and optimized with respect to the localization task. Initial experiments are carried out on an aluminum structure, where holes were drilled to simulate the presence of damage. The results show very good agreement between the calculated and actual positions of the damage.

Lamb Wave-Mode Tuning of Piezoelectric Wafer Active Sensors for Structural Health Monitoring

Abstract: An analytical and experimental investigation of the Lamb wave-mode tuning with piezoelectric wafer active sensors (PWASs) is presented. The analytical investigation assumes a PWAS transducer bonded to the upper surface of an isotropic flat plate. Shear lag transfer of tractions and strains is assumed, and an analytical solution using the space-wise Fourier transform is reviewed, closed-form solutions are presented for the case of ideal bonding (i.e., load transfer mechanism localized at the PWAS boundary). The analytical solutions are used to derive Lamb wave-mode tuning curves, which indicate that frequencies exist at which the AO mode or the SO mode can be either suppressed or enhanced. Extensive experimental tests that verify these tuning curves are reported. The concept of "effective PWAS dimension" is introduced to account for the discrepancies between the ideal bonding hypothesis and the actual shear-lag load transfer mechanism. The paper further shows that the capability to excite only one desired Lamb wave mode is critical for practical structural health monitoring (SHM) applications such as PWAS phased array technique (e.g., the embedded ultrasonics structural radar (EUSR)) and the time reversal process (TRP). In PWAS phased array EUSR applications, the basic assumption of the presence of a single low-dispersion Lamb wave mode (SO) is invoked since several Lamb wave modes traveling at different speeds would disturb the damage imaging results. Examples are given of correctly tuned EUSR images versus detuned cases, which illustrate the paramount importance of Lamb wave-mode tuning for the success of the EUSR method. In the TRP study, an input wave packet is reconstructed at a transmission PWAS when the signal recorded at the receiving PWAS is reversed in the time domain and transmitted back to the original PWAS. Ideally, TRP could be used for damage detection without a prior baseline. However, the application of TRP to Lamb waves SHM is impended by the dispersive and multimodal nature of the Lamb waves. The presence of more then one mode usually produces additional wave packets on both sides of the original wave packet due to the coupling of the Lamb wave modes. The PWAS Lamb wave tuning technique described in this paper is used to resolve the side packets problem. Several tuning cases are illustrated. It is found that the 30 kHz tuning of the AO Lamb wave mode with a 16-count smoothed tone burst leads to the complete elimination of the side wave packets. However, the elimination was less perfect for the 290 kHz tuning of the SO mode due to the frequency sidebands present in the tone-burst wave packet.

Assessing the reliability of the modified three-component spatial autocorrelation technique

Abstract: SUMMARY Analysis of seismic ambient vibrations is becoming a widespread approach to estimate subsurface shear wave velocity profiles. However, the common restriction to vertical component wavefield data does not allow investigations of Love wave dispersion and the partitioning between Rayleigh and Love waves. In this study we extend the modified spatial autocorrelation technique (MSPAC) to three-component analysis (3c-MSPAC). By determination of Love wave dispersion curves, this technique provides additional information for the determination of shear wave velocity–depth profiles. Furthermore, the relative fraction of Rayleigh waves in the total portion of surface waves on the horizontal components is estimated. Tests of the 3c-MSPAC method are presented using synthetic ambient vibration waveform data. Different types of surface waves are simulated as well as different modes. In addition, different spatial distributions of sources are used. We obtain Rayleigh and Love wave dispersion curves for broad frequency bands in agreement with the models used for waveform simulation. The same applies for the relative fraction of Rayleigh waves. Dispersion curves are observed at lower frequencies for Love waves than for Rayleigh waves. While 3c-MSPAC has clear advantages for determination of Love waves velocities, 3c-MSPAC and conventional vertical frequency–wavenumber analysis complement each other in estimating the Rayleigh wave dispersion characteristics. Inversions of the dispersion curves for the shear wave velocity–depth profile show that the use of Love wave velocities confirms the results derived from Rayleigh wave velocities. In the presence of higher mode surface waves, Love waves even can improve results. Application of 3c-MSPAC to ambient vibration data recorded during field measurements (Pulheim, Germany) show dominance of Love waves in the wavefield. Existing shear wave profiles for this site are consistent with models obtained from inversion of Rayleigh and Love wave dispersion curves.

The response of rectangular piezoelectric sensors to Rayleigh and Lamb ultrasonic waves

Abstract: A fundamental understanding of the response of piezoelectric transducer patches to ultrasonic waves is of increasing interest to the field of structural health monitoring While analytical solutions exist on the interaction of a piezoelectric actuator with the generated Lamb waves, the behavior of a piezoelectric sensor has only been examined for the limited case of a piezo-actuated Lamb wave in a pitch-catch configuration This paper focuses on the fundamental response of surface-bonded piezoelectric sensors to ultrasonic waves The response to both Rayleigh waves and Lamb waves is examined, starting with harmonic excitation fields and moving to broadband and narrowband excitation fields General oblique incidence of the wave on rectangular sensors is treated first; parallel incidence is then derived as a particular case The solutions are developed analytically for the harmonic and the narrowband excitations, and semianalytically for the broadband excitation The results obtained can be used to design u

Local and noncontact measurements of bulk acoustic wave velocities in thin isotropic plates and shells using zero group velocity Lamb modes

Abstract: An original method for material characterization with acoustic waves is presented. The measurement of the longitudinal and shear wave velocities in thin isotropic plates or shells is performed locally on the same face without any mechanical contact. We exploit the resonance that occurs at the minimum frequency thickness product of the first order symmetric (S1) and of the second order antisymmetric (A2) Lamb modes. At these frequencies the group velocity vanishes, whereas the phase velocity remains finite. Then, the energy, which cannot propagate in the structure, is localized in a zone of diameter half the wavelength. The vibrations are excited in the thermoelastic regime by a laser pulse and detected at the same point by an optical interferometer. For these two Lamb modes we have computed the variations of the frequency thickness product versus Poisson’s ratio. The resonance frequency ratio, which is independent of the plate or shell thickness, provides an absolute and local measurement of Poisson’s rat...

Lamb wave propagation modelling for damage detection: I. Two-dimensional analysis

Abstract: Wave propagation modelling is important for reliable damage detection based on Lamb waves. A number of different numerical computational techniques have been developed for wave propagation studies. The local interaction simulation approach, used for modelling sharp interfaces and discontinuities in complex media, has been applied effectively for numerical simulations of elastic wave interaction with structural damage. The paper builds upon this experience and reports numerical investigations of Lamb wave propagation modelling for damage detection in metallic structures. The ultimate objective of the investigations is to demonstrate that numerical simulations can significantly ease the monitoring strategy used for damage detection with Lamb waves. The interaction of fundamental Lamb wave modes with a rectangular damage slot in an aluminium plate is investigated as an example. For the sake of completeness, the first part of the paper forms an introduction to wave propagation studies for damage detection. The local interaction simulation approach is implemented. This is followed by a series of two-dimensional studies of wave interaction with damage.

Micromachined thin film plate acoustic resonators utilizing the lowest order symmetric lamb wave mode

Abstract: Thin film integrated circuits compatible resonant structures using the lowest order symmetric Lamb wave propagating in thin aluminum nitride (AlN) film membranes have been studied. The 2-mum thick, highly c-oriented AlN piezoelectric films have been grown on silicon by pulsed, direct-current magnetron reactive sputter deposition. The films were deposited at room temperature and had typical full-width, half-maximum value of the rocking curve of about 2 degrees. Thin film plate acoustic resonators were designed and micromachined using low resolution photolithography and deep silicon etching. Plate waves, having a 12-mum wavelength, were excited by means of both interdigital (IDT) and longitudinal wave transducers using lateral field excitation (LW-LFE), and reflected by periodical aluminum-strip gratings deposited on top of the membrane. The existence of a frequency stopband and strong grating reflectivity have been theoretically predicted and experimentally observed. One-port resonator designs having varying cavity lengths and transducer topology were fabricated and characterized. A quality factor exceeding 3000 has been demonstrated at frequencies of about 885 MHz. The IDT based film plate acoustic resonators (FPAR) technology proved to be preferable when lower costs and higher Qs are pursued. The LW-LFE-based FPAR technology offers higher excitation efficiency at costs comparable to that of the thin film bulk acoustic wave resonator (FBAR) technology

Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones.

Abstract: The use of guided waves has recently drawn significant interest in the ultrasonic characterization of bone aiming at supplementing the information provided by traditional velocity measurements. This work presents a three-dimensional finite element study of guided wave propagation in intact and healing bones. A model of the fracture callus was constructed and the healing course was simulated as a three-stage process. The dispersion of guided modes generated by a broadband 1-MHz excitation was represented in the time-frequency domain. Wave propagation in the intact bone model was first investigated and comparisons were then made with a simplified geometry using analytical dispersion curves of the tube modes. Then, the effect of callus consolidation on the propagation characteristics was examined. It was shown that the dispersion of guided waves was significantly influenced by the irregularity and anisotropy of the bone. Also, guided waves were sensitive to material and geometrical changes that take place during healing. Conversely, when the first-arriving signal at the receiver corresponded to a nondispersive lateral wave, its propagation velocity was almost unaffected by the elastic symmetry and geometry of the bone and also could not characterize the callus tissue throughout its thickness. In conclusion, guided waves can enhance the capabilities of ultrasonic evaluation.

Piezoelectric transducer arrangement for the inspection of large composite structures

Abstract: The aim of the present work is to develop a system of smart devices that could be permanently attached on the surface of the composite structure and monitor the interaction of low-frequency Lamb waves with defects. A linear array of transmitters would generate a relatively uniform wavefront allowing the inspection of large areas with a limited number of sensors. The asymmetric A0 Lamb mode is generated in carbon fibre reinforced plastic (CFRP) quasi-isotropic laminates using an array of thin piezoceramic transmitters operating in-phase. In this paper, the effect of damage size on the propagation of Lamb waves is presented. Experimental verification is also presented in multidirectional CFRP composite panels. Critical size impact damage is detected. Finally, the technique is applied to a stiffened panel. Damage on the skin or flange is detectable while damage on the web or cap is not detected with the current experimental set up.

Lamb wave propagation modelling for damage detection: II. Damage monitoring strategy

Abstract: Wave propagation modelling is important for reliable damage detection based on Lamb waves. A number of different numerical computational techniques have been developed for wave propagation studies. The local interaction simulation approach, used for modelling sharp interfaces and discontinuities in complex media, has been applied effectively for numerical simulations of elastic wave interaction with structural damage. The paper builds upon this experience and reports numerical investigations of Lamb wave propagation modelling for damage detection in metallic structures. The ultimate objective of these investigations is to demonstrate that numerical simulations can significantly ease the monitoring strategy used for damage detection with Lamb waves. The interaction of fundamental Lamb wave modes with a rectangular damage slot in an aluminium plate is investigated as an example. The second part of the wave propagation studies focuses on the monitoring strategy for damage detection. The effect of sensor position on the amplitude and time of flight of Lamb waves is investigated and discussed for various severities of damage. The results are validated experimentally.

Finite element modeling and experimental characterization of crosstalk in 1-D CMUT arrays

Abstract: Crosstalk is the coupling of energy between the elements of an ultrasonic transducer array. This coupling degrades the performance of transducers in applications such as medical imaging and therapeutics. In this paper, we present an experimental demonstration of guided interface waves in capacitive micromachined ultrasonic transducers (CMUTs). We compare the experimental results to finite element calculations using a commercial package (LS-DYNA) for a 1-D CMUT array operating in the conventional and collapsed modes. An element in the middle of the array was excited with a unipolar voltage pulse, and the displacements were measured using a laser interferometer along the center line of the array elements immersed in soybean oil. We repeated the measurements for an identical CMUT array covered with a 4.5-mum polydimethyl-siloxane (PDMS) layer. The main crosstalk mechanism is the dispersive guided modes propagating in the fluid-solid interface. Although the transmitter element had a center frequency of 5.8 MHz with a 130% fractional bandwidth in the conventional operation, the dispersive guided mode was observed with the maximum amplitude at a frequency of 2.1 MHz, and had a cut-off frequency of 4 MHz. In the collapsed operation, the dispersive guided mode was observed with the maximum amplitude at a frequency of 4.0 MHz, and had a cut-off frequency of 10 MHz. Crosstalk level was lower in the collapsed operation (-39 dB) than in the conventional operation (-24.4 dB). The coverage of the PDMS did not significantly affect the crosstalk level, but reduced the phase velocity for both operation modes. Lamb wave modes, A0 and S0, were also observed with crosstalk levels of -40 dB and -65 dB, respectively. We observed excellent agreement between the finite element and the experimental results

Reconstruction of Rayleigh Lamb dispersion spectrum based on noise obtained from an air-jet forcing

Abstract: The time-domain cross correlation of incoherent and random noise recorded by a series of passive sensors contains the impulse response of the medium between these sensors. By using noise generated by a can of compressed air sprayed on the surface of a plexiglass plate, we are able to reconstruct not only the time of flight but the whole wave forms between the sensors. From the reconstruction of the direct A0 and S0 waves, we derive the dispersion curves of the flexural waves, thus estimating the mechanical properties of the material without a conventional electromechanical source. The dense array of receivers employed here allow a precise frequency-wavenumber study of flexural waves, along with a thorough evaluation of the rate of convergence of the correlation with respect to the record length, the frequency, and the distance between the receivers. The reconstruction of the actual amplitude and attenuation of the impulse response is also addressed in this paper.