Showing papers on "Lamb waves published in 1997"

Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms

Abstract: 1 Spectral Analysis of Wave Motion.- 1.1 Continuous Fourier Transforms.- 1.2 Discrete Fourier Transform.- 1.3 Examples Using the FFT Algorithm.- 1.4 Experimental Aspects of Wave Signals.- 1.5 Spectral Analysis of Wave Motion.- 1.6 Propagating and Reconstructing Waves.- Problems.- 2 Longitudinal Waves in Rods.- 2.1 Elementary Rod Theory.- 2.2 Basic Solution for Waves in Rods.- 2.3 Dissipation in Rods.- 2.4 Coupled Thermoelastic Waves.- 2.5 Reflections and Transmissions.- 2.6 Distributed Loading.- Problems.- 3 Flexural Waves in Beams.- 3.1 Bernoulli-Euler Beam Theory.- 3.2 Basic Solution for Waves in Beams.- 3.3 Bernoulli-Euler Beam with Constraints.- 3.4 Reflection of Flexural Waves.- 3.5 Curved Beams and Rings.- 3.6 Coupled Beam Structure.- Problems.- 4 Higher-Order Waveguides.- 4.1 Waves in Infinite Media.- 4.2 Semi-Infinite Media.- 4.3 Doubly Bounded Media.- 4.4 Doubly Bounded Media: Lamb Waves.- 4.5 Hamilton's Principle.- 4.6 Modified Beam Theories.- 4.7 Modified Rod Theories.- Problems.- 5 The Spectral Element Method.- 5.1 Structures as Connected Waveguides.- 5.2 Spectral Element for Rods.- 5.3 Spectral Element for Beams.- 5.4 General Frame Structures.- 5.5 Structural Applications.- 5.6 Waveguides with Varying Cross Section.- 5.7 Spectral Super-Elements.- 5.8 Impact Force Identification.- Problems.- 6 Waves in Thin Plates.- 6.1 Plate Theory.- 6.2 Point Impact of a Plate.- 6.3 Wavenumber Transform Solution.- 6.4 Waves Reflected from a Straight Edge.- 6.5 Scattering of Flexural Waves.- 6.6 Lateral Boundary Conditions.- 6.7 Curved Plates and Shells.- Problems.- 7 Structure-Fluid Interaction.- 7.1 Acoustic Wave Motion.- 7.2 Plate-Fluid Interaction.- 7.3 Double Panel Systems.- 7.4 Waveguide Modeling.- 7.5 Radiation from Finite Plates.- 7.6 Cylindrical Cavity.- Problems.- 8 Thin-Walled Structures.- 8.1 Membrane Spectral Elements.- 8.2 Spectral Elements for Flexure.- 8.3 Folded Plate Structures.- 8.4 Structural Applications.- 8.5 Segmented Cylindrical Shells.- 8.6 Future of Spectral Elements.- Problems.- Afterword.- Appendix: Bessel Functions.- References.

Elastic wave band gaps and defect states in two-dimensional composites

Abstract: Using the plane-wave expansion method, we study the propagation of elastic waves through two-dimensional (2-D) periodic composites which exhibit full band gaps for all the polarizations and directions of the displacements. Defect states created inside those band gaps are also studied by disturbing the periodicity of the lattice. Systems exhibiting such kinds of states can be used as acoustical filters.

Long range propagation of Lamb waves in chemical plant pipework

Abstract: Site trials ofa dry coupled piezoelectric transducer system designed to detect corrosion in chemical plant pipework using cylindrical Lamb waves are described. The L(0,2) Lamb mode has been successfully propagated over distances approaching 50 m (160 ft; equivalent to 100 m [320 ft] round trip in pulse echo mode) in 152 mm (6 in.) diameter steel pipes in operating chemical plants. An excitation and reception system has also been developed which gives uni-directional propagation of the L(0,2) mode. The effect of welds, flanges and pipe supports was similar to that seen in earlier laboratory studies. The system was used successfully on painted and insulated pipes carrying both gases and low viscosity liquids.

Lamb wave scattering analysis for reflector characterization

Abstract: The potential use of guided waves for defect characterization is studied. The influence of defect shape and size on transmitted and reflected fields is considered. Using the hybrid boundary element technique, the reflection and transmission coefficients for selected guided wave modes are numerically calculated and compared to experimental data. Selecting the aspect ratio as a shape parameter for various defects, the transmission and reflection coefficients are measured for certain guided wave modes input to the defect. The influence of defect size is then studied by monitoring the transmission and reflection coefficients for defects of various shapes and depths. The studies presented indicate that defect characterization is possible if a proper mode selection criteria can be established. The suitable features related to transmission and reflection coefficient data can also be used for algorithm development and implementation purposes of defect characterization.

Microfabricated Lamb wave device based on PZT sol-gel thin film for mechanical transport of solid particles and liquids

Abstract: The fabrication using silicon micromachining and characterization of an acoustic Lamb wave actuator is presented. The intended use of the device is for mass transport and sensor applications. The device consists of dual interdigitated transducers patterned on a thin-film composite membrane of silicon nitride, platinum, and a sol-gel-derived piezoelectric ceramic (PZT) thin film. The acoustic properties of the device are presented along with preliminary applications to mechanical transport and liquid delivery systems. Improved acoustic signals and improved mass transport are achieved with PZT over present Lamb wave devices utilizing ZnO or AlN as the piezoelectric transducer.

Piezoelectric transducer embedded in a composite plate: Application to Lamb wave generation

Abstract: The aim of this paper is to show that Lamb waves may be effectively generated using piezoelectric transducers embedded inside a composite plate, for nondestructive evaluation and health monitoring applications. A cylindrical transducer embedded in a composite host plate is considered. The electrical impedance of the transducer alone in vacuum and then of the embedded transducer, which allows the identification of the resonance modes, have been obtained by the finite element method (FEM). Moreover, the displacement fields in the plate, which allow the identification of the types of Lamb waves, have been computed at the resonance frequencies. Comparison between the FEM results and the Lamb wave dispersion curves of the host material are in good agreement. Experimental results (electrical impedance, frequency response, and phase velocities) concerning a composite plate specimen containing the same piezoelectric transducer inside it are shown. A good agreement is generally obtained between numerical and exper...

Wavelet signal processing for enhanced Lamb-wave defect detection in composite plates using optical fiber detection

Abstract: A wavelet-transform-based technique to enhance defect de- tection in a carbon fiber composite plate interrogated using ultrasonic Lamb waves and incorporating an optical fiber receiver is described. Fundamental symmetric (S0) Lamb waves were introduced into the sample plates using a conventional piezoelectric transducer operating at a frequency of around 250 kHz. Coupling into the plates was achieved using a perspex phase-matching wedge. The propagating acoustic pulses were monitored using a simple embedded or surface-mounted singlemode optical fiber forming the signal arm of an optical fiber Mach- Zehnder interferometer. The direct Lamb wave reflections from delami- nations in the sample plates were of low amplitude, although a degree of defect visibility enhancement was achieved by correlating the received signals with the outgoing ultrasonic pulse. A considerable improvement in the defect visibility over the latter technique was found by using a wavelet-transform-based novelty technique to identify the defective plate zones. Using an orthogonal wavelet transform to compress the data, important structurally related features were extracted by setting appro- priate threshold levels on the wavelet coefficients. The reconstructed (uncompressed) data from defect-free portions of the plate were used to construct a template representing a normal condition. Defect location was achieved by analysis of the departure of signals arising from defec- tive plate regions from the no-fault condition template. © 1997 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(97)00507-2)

Excess attenuation of leaky Lamb waves due to viscous fluid loading

Abstract: In two recent papers [J. Acoust. Soc. Am. 97, 3191–3193 (1995) and 98, 1057–1064 (1995)], Zhu and Wu presented an analytical technique to assess the effect of viscous fluid loading on the propagation properties of Rayleigh and Lamb waves in fluid-loaded solids. They modeled the viscous fluid as a hypothetical isotropic solid having rigidity c55=−iωη, where η denotes the viscosity of the fluid and ω is the angular frequency. In this way, the vorticity mode associated with the viscosity of the fluid is formally described as the shear-mode in the fictitious solid. In this paper this technique is further developed by removing certain inconsistencies that unnecessarily reduce the accuracy and the range of validity of Zhu and Wu’s results. By properly accounting for viscous effects on the bulk compressional wave in the fluid and applying a rigorous treatment of the field equations and boundary conditions, the exact dispersion equations that are not limited to low frequencies and viscosities are derived. Example...

Apparatus and method for characterizing semiconductor wafers during processing

Abstract: An apparatus and method are disclosed for characterizing semiconductor wafers or other test objects that can support acoustic waves. Source and receiving transducers are configured in various arrangements to respectively excite and detect acoustic waves (e.g., Lamb waves) in a wafer to be characterized. Signals representing the detected waves are digitally processed and used to compute a measurement set correlated with the waves' velocity in the wafer. A characterization sensitivity is provided that describes how different wafer characteristics of interest vary with changes in the propagation of the acoustic waves. Using the characterization sensitivity and measurement sets computed at a setup time when all wafer characteristics are known and one or more process times when at least one of the characteristics is not known the perturbation in wafer characteristics between the setup and the process times can be determined. Characterization accuracy is improved by a wafer calibration procedure wherein measurement offsets from known conditions are determined for each wafer being characterized. An apparatus and technique are disclosed for correcting for anisotropy of acoustic wave velocity due to the direction of wave propagation with respect to a preferred crystallographic axis of the wafer. An apparatus and technique are also described for measuring wafer temperature using a single transducer whose temperature is related to the temperature of the wafer and, optionally, resonator structures. For characterization steps that occur when the wafer is chucked, a chuck structure is described that reduces the likelihood of the chuck interfering with the waves in the wafer.

Air-coupled Lamb wave tomography

Abstract: An entirely air-coupled inspection system using a pair of micromachined silicon capacitance transducers has been used to image defects in thin plates of different materials (0.7 mm to 2.22 mm thick) using air-coupled Lamb wave tomography. A filtered back projection algorithm was used in a form of difference tomography to reconstruct images of defects up to 10 mm diameter machined in aluminium and perspex (Plexiglas) plates, as well as in samples of carbon fiber reinforced polymer (CFRP). The technique was able to resolve non-central defects as well as multiple flaws within the scan area. This flexible tomographic system was able to produce images of the change in a variety of different acoustic variables from only one set of experimental data, with success dependent on the size, shape, and location of the defect in the scan area.

Modal analysis of Lamb wave generation in elastic plates by liquid wedge transducers

Abstract: A modal analysis is presented to describe the excitation of Lamb waves in an elastic plate using a liquid wedge transducer. Analytical expression for the displacement of a given mode is derived for the excitation by a uniform bounded beam. In contrast to previous studies, the contribution of the reflected wave is included in the input exciting forces using a perturbation theory. The conversion efficiency, defined as the ratio of the guided mode power to the incident power, is related to a single parameter which depends on the rate of attenuation due to leakage from the guided wave into the liquid wedge. Numerical results relevant to the fundamental Lamb modes are obtained as a function of frequency for various incident beam widths and plate thickness. Using optical interferometric detection, direct measurements of the Lamb modes displacements have been carried out in aluminium plates to verify the theoretical analysis.

Self-Focusing of Rayleigh Waves and Lamb Waves with a Linear Phased Array

Abstract: A simple idea for self-focusing of a linear array has been extended to Rayleigh and Lamb waves. The self-focusing procedure first measures the backscattered signals for a first transmission by a single element of the array. A cross-correlation technique is used to determine the time-of-flight differences of the backscattered signals received by the elements of the array. These time delays are used to adjust the times of excitation of the elements for transmission focusing on the defect. Using the differences in arrival time once more, the backscattered signals after transmission focusing are aligned for reception focusing. Experimental results demonstrate the ability to self-focus on single defects. For multiple defects, the technique has been extended to focus on the defect that produces the largest backscattered signal.

Acoustic Emission Source Location Using Lamb Wave Modes

Abstract: This paper describes the development of a technique based on acoustic emission (AE) technology that can be used for global nondestructive evaluation (NDE) of steel structures. This will also be useful for the subsequent local inspection used to further monitor cracking, defective connections, retrofit measures, and so forth. The dispersive nature of Lamb wave propagation in plates makes it possible to perform a linear source location of AE events based on the arrival of different frequency components (Lamb wave modes) of an AE event at a single transducer. Experiments on steel beams and plates in the laboratory explored the theory of wave propagation and digital signal processing needed to pursue this objective. Subsequent field investigation on a real bridge substantiated the applicability of this technique. This new technique could allow AE inspection to locate structural problems better, and with a reduced number of transducers.

Lamb wave excitation by Hertzian contacts with applications in NDE

Abstract: Excitation of Lamb waves in solid plates by point-like Hertzian contacts for material characterization and nondestructive testing is investigated. A 2 dimensional model using normal mode theory is used to predict the relative excitation efficiency of the lowest order Lamb waves in anisotropic solid plates. Hertzian contact transducers with PZT-5H piezoelectric material and quartz buffer rods are realized to operate in the 200 to 500 kHz range for experimental verification. Single mode operation with the lowest order antisymmetric Lamb wave (A/sub 0/) mode is achieved in various plates at in agreement with theoretical predictions. The technique is applied for material characterization on single crystal silicon samples and defect detection in composite plates. The phase velocity anisotropy of the A/sub 0/ mode is measured with signal-to-noise levels exceeding 65 dB. In (111) cut silicon plates the absolute phase velocity is measured with /spl plusmn/0.05% accuracy. The phase velocity anisotropy and effects of delamination in layered composite plates are calculated using the surface impedance approach. The experiments on graphite/epoxy composite plates agree with these calculations and show the potential of the method for defect detection with high resolution.

Lamb waves in piezoelectric focused radiator as a reason for discrepancy between O’Neil’s formula and experiment

Abstract: One of the well-known methods of ultrasound focusing is the use of a transducer having the form of a concave spherical cap In the theoretical analysis, O’Neil’s formula is widely used, which describes acoustic pressure on the axis of the transducer under the assumption that normal velocity of its surface is uniform Usually, it is believed that modern piezoelectric focused sources are very close to this theoretical model The paper presented describes results of experimental investigation which showed that there exists a significant disagreement between the observed acoustic field and that predicted by the theory of O’Neil Two types of measurements have been made to clarify this problem The acoustic pressure field of a focused piezoceramic transducer (with aperture diameter of 100 mm, radius of curvature of 100 mm, resonance frequency of 1 MHz) has been measured in a water tank using a miniature hydrophone In addition, the radiator surface vibration has been studied in air using an optical interferome

Modal analysis of acoustic emission signals

Abstract: This report shows the results of a continuing study to determine the type of waves present in plates of different thickness created by breaking pencil leads in-plane (IP) and out-of-plane (OOP) on the plates and by detecting the resulting stress waves with a high fidelity acoustic-emission transducer mounted on the edge and surface of the plates. The results show that the extensional velocity over the range of plate thickness from 3.13 to 12.5 mm does not change, and the flexure wave is dispersive in accordance with plate wave theory. The procedure in this work split the signal into two frequency ranges, a high frequency range with a 100 kHz high-pass filter and a low frequency range with a 20-70 kHz bandpass filter. This frequency split provided an easy method of measuring the velocity of the low frequency flexure wave. A bulk shear wave, not predicted by plate wave theory was observed along with the extensional wave in the high frequency channel. In order to confirm the presence of the shear wave, two shear plates, one with particle motion vertical to the plane of the plate and the other parallel to the plane of the plate were attached to the end of one of the bars. These transducers were used as receivers for IP and OOP pencil-lead breaks, and also as transmitters excited by a 150-V spike pulse. Both the Sv and Sh waves, created with pulsing, could be detected with a transducer mounted on the surface with petroleum jelly. The Sh wave had a much higher amplitude than the Sv wave. The results show that mode conversion of the Sv wave to a flexure wave occurs, as it propagates down the bar, which partially accounts for its loss of amplitude. From this study, it is suggested that the crack growth signal detected by most AE tests on large thin-wall structures utilizing 100 kHz high-pass filtering, resonant transducers, and large transducer spacing, is the Sh wave created by crack propagation.

Diffraction of P, S and Rayleigh waves by three-dimensional topographies

Abstract: SUMMARY The diffraction of P, S and Rayleigh waves by 3-D topographies in an elastic halfspace is studied using a simplified indirect boundary element method (IBEM). This technique is based on the integral representation of the diffracted elastic fields in terms of single-layer boundary sources. It can be seen as a numerical realization of Huygens’ principle because diffracted waves are constructed at the boundaries from where they are radiated by means of boundary sources. A Fredholm integral equation of the second kind for such sources is obtained from the stress-free boundary conditions. A simplified discretization scheme for the numerical and analytical integration of the exact Green’s functions, which employs circles of various sizes to cover most of the boundary surface, is used. The incidence of elastic waves on 3-D topographical profiles is studied. We analyse the displacement amplitudes in the frequency, space and time domains. The results show that the vertical walls of a cylindrical cavity are strong diffractors producing emission of energy in all directions. In the case of a mountain and incident P, SV and SH waves the results show a great variability of the surface ground motion. These spatial variations are due to the interference between locally generated diffracted waves. A polarization analysis of the surface displacement at different locations shows that the diffracted waves are mostly surface and creeping waves.

Compact phase-shifted Sagnac interferometer for ultrasound detection

Abstract: A compact fibre, phase-shifted Sagnac interferometer for ultrasound detection has been developed. The interferometer is a truly path-matched device, and therefore requires no path stabilization or heterodyning. It is a less expensive and more robust alternative to the heterodyne or path-stabilized Michelson interferometer. The device provides high spatial resolution of ultrasonic detection. It has been used in conjunction with conventional piezoelectric transducers (PZT) to detect Rayleigh and Lamb waves and to image a crack in a thin plate, rivet cracks in riveted plates, and for ultrasonic beam profiling.

Elastic guided waves in plates with surface roughness. I. Model calculation

Abstract: This paper reports analytical research on the effect of surface roughness on ultrasonic guided waves in plates. The theoretical model is constructed by exploiting the phase-screen assumption that takes advantage of the Kirchhoff approximation, where, on a local scale, the roughness degrades only the signal phase. The effect of the rough surface on the guided wave is treated by decomposing the wave modes into their constituent partial waves and considering individually the effect of the roughness on the partial wave components as they reflect from the plate surfaces. An approximate dispersion relation is derived for the traction-free rough waveguide that is formally identical to the conventional Lamb wave equation, but incorporating the roughness parameter as a complex plate thickness. A more accurate version of the model calculation is generalized to fluid-immersed plates having only a single rough surface either on the same, or opposite, side of the plate as the incident ultrasonic field. Calculations of the reflection coefficients in the presence of roughness serve to illustrate the phenomena for the case of the guided waves.

Magnetoacoustic surface waves in magnetic crystals near spin-reorientation phase transitions

Abstract: Theoretical and experimental work on magnetoacoustic surface waves in ferro- and antiferromagnets is reviewed Results on the propagation of Rayleigh and Lamb magnetoelastic waves in a plate are presented within the framework of a rotation- and translation-invariant theory Spectra of the shear surface magnetoacoustic waves (SSMAWs) caused by effects of magnetostriction and piezomagnetism are also considered with emphasis on the vicinity of reorientation phase transitions The problem types of soft modes involved in phase transitions is discussed in detail A comparison is made of experimental results and theoretical predictions on the propagation of Rayleigh waves in magnetic materials

Lamb waves generated by complex harmonic inhomogeneous plane waves

Abstract: This paper presents a theoretical investigation of the generation of Lamb waves inside an immersed plate by complex harmonic inhomogeneous plane waves. Whereas free modes of a fluid-loaded plate are classically assumed to be formed by inhomogeneous plane waves with real frequency (leaky waves), the nature of Lamb waves is searched in this study in terms of combinations of transient inhomogeneous plane waves characterized by a complex slowness vector and a complex frequency. It is shown that dispersion curves of transient Lamb waves (only the frequency is complex) can be very different from the dispersion curves of permanent leaky waves (only the slowness is complex), especially for the A0 and S0 modes for which there exists a cut-off frequency beyond which these modes do not exist. In the general case, when both the frequency and the slowness are complex, connections between modes clearly appear from the calculation of dispersion curves.

Theory for the time evolution of nonlinear Rayleigh waves in an isotropic solid

Abstract: The evolution equations for the Rayleigh wave are derived with a single physical assumption that the cumulative effect of weak nonlinear interactions leads to a slow variation of the wave both in time and space. This solution of a classical problem of elasticity theory reveals that along with wave spectrum broadening induced by nonlinear processes (also characteristic of plane bulk pressure waves), wave spectrum narrowing may be induced by the additional nonlinear processes resulting from Rayleigh wave confinement near the surface.

Ultrasonic condition monitoring of composite structures using a low-profile acoustic source and an embedded optical fiber sensor

Abstract: The purpose of this paper is to provide a concise introduction to the developments and recent findings of a BRITE-EURAM program of work (BRE2.CT94-0990 , Structurally Integrated System for the comprehensive evaluation of COmposites). The aim of the program has been to develop an acoustic/ultrasonic based structural monitoring system for composite structures using material compatible sensors. Since plate-like structures have been investigated, it has been a requirement to utilise the propagation of ultrasonic Lamb waves through the sample materials. Preliminary investigations utilised conventional piezo-electric sources coupled to the sample via perspex wedges. The Lamb waves generated by these sources were monitored using either a fully embedded or surface mounted optical fibre sensors. The system was tested with a variety of different carbon and glass fibre reinforced panels, and the interaction of the Lamb waves with different defects in these materials was monitored. Conventional signal processing allowed the location of defects such as impact damage sites, delaminations and holes. Subsequent investigations have endeavoured to refine the system. This paper reports the development of advanced wavelet based signal processing techniques to enhance defect visibility, the optical connectorisation of composite panels, and the development of flexible low profile acoustic sources for efficient Lamb wave generation.