Showing papers on "Lamb waves published in 1995"

Sensors based on piezoelectric resonators

Abstract: A review of sensors based on piezoelectric crystal resonators is presented. The survey focuses on the fundamental resonator modes rather than on the variety of surrounding support configurations in special sensor applications. First, the general properties of vibrating crystal sensors and their inherent superiority are described. The sensor concepts utilizing either homogeneous resonators with temperature and pressure (stress) as primary measurants or composite resonators with areal mass density and viscoelastic properties of the 'foreign' layer as primary measurands are discriminated. A comparison between bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators with respect to their primary sensitivity functions and principal capabilities for sensor applications is given and the importance of recent investigations on Lamb wave and horizontal polarized shear wave (HPLW) interdigital transducer (IDT) resonators is acknowledged. The importance of mode purity for high dynamic range sensors based on resonators and some aspects of the demand on specialized electronics are emphasized. The present state of established sensors based on primary sensitivities, e.g., quartz-crystal thermometers, pressure transducers, thin-film thickness and deposition-rate monitors, viscoelastic layer analysers (crystal/liquid composite resonators) is reviewed. A selection of the most promising recently investigated vibrating crystal sensors utilizing indirect sensitivities is described, including the wide field of analyte-selective coatings and resonator-based immunosensors or immunoassays. Finally, the potential of alternative piezoelectric materials for future sensor developments is briefly discussed.

Wave propagation in layered anisotropic media : with applications to composites

Abstract: Introduction - historical background. Part 1 Field equations and tensor analysis: the stiffness tensor material symmetry matrix forms of stiffness engineering constants transformed equations expanded field equations planes of symmetry. Part 2 Bulk waves: an overview the Christoffel equation material symmetry computer aided analysis group velocity energy flux. Part 3 Generalized Snell's law and interfaces: boundary conditions characterization of incident waves critical angles two fluid media two isotropic media. Part 4 Formal solutions: common form of solutions triclinic layer the monoclinic case higher symmetry materials formal solutions in fluid media the alpha-c relation and the Christoffel equation. Part 5 Scattered wave amplitudes: notation reflection from a free surface scattering from fluid-solid interfaces scattering from solid-solid interface. Part 6 Interface waves: surface waves pseudo-surface waves Scholte waves. Part 7 Free wave in plates: free waves in triclinic plates free waves in monoclinic plates higher symmetry material plates numerical computation strategy. Part 8 General layered media: geometric description of unit cell analysis properties of the transfer matrix free waves on the layered cell waves in a periodic medium bottom bounding solid substrate. Part 9 Propagation along axes of symmetry: geometry SH waves motion in the sagittal plane free waves on the layered cell waves in a periodic medium bottom bounding solid substrate. Part 10 Fluid-loaded solids: reflection from a substrate plates completely immersed in fluids higher symmetry cases leaky waves experimental technique. Part 11 Piezoelectric effects: basic relations of piezoelectric materials simplified field equations analysis formal solutions higher symmetric materials remarks on the monoclinic-m case reflection and transmission coefficients sample illustration remarks on layered piezoelectric media. Part 12 Transient waves: theoretical development source characterization integral transforms of formal solutions isotropic media anisotropic media Cagniard-de Hoop transformation semi-space media. Part 13 Scattering from layered cylinders: field equations formal solutions in isotropic cylinders characterization of incident waves formal solutions for a layer scattering amplitudes. Part 14 Elastic properties of composites: general description of fibrous composites the model the layered model the square fibrous case anisotropic fibre and matrix strain energy approach undulated fibre appendix.

Three‐dimensional instabilities of film flows

Abstract: Two‐dimensional (2‐D) interfacial waves on flowing films are unstable with respect to both two‐ and three‐dimensional instabilities. In this paper, several distinct three‐dimensional instabilities that occur in different regions of the parameter space defined by the Reynolds numberR and the frequency f of forced two‐dimensional waves are discussed in detail. (a) A synchronous 3‐D instability, in which spanwise deformations of adjacent wave fronts have the same transverse phase, appears over a wide range of frequency. These transverse modulations occur mainly along the troughs of the primary waves and eventually develop into sharp and nearly isolated depressions. The instability involves many higher harmonics of the fundamental 2‐D waves. (b) A 3‐D surbharmonic instability occurs for frequencies close to the neutral curve f c (R). In this case, the transverse modulations are out of phase for successive wave fronts, and herringbone patterns result. It is shown that this weakly nonlinear instability is due to the resonant excitation of a triad of waves consisting of the fundamental two‐dimensional wave and two oblique waves. The evolution of wavy films after the onset of either of these 3‐D instabilities is complex. However, sufficiently far downstream, large‐amplitude solitary waves absorb the smaller waves and become dominant.

Applications of micromachined capacitance transducers in air-coupled ultrasonics and nondestructive evaluation

Abstract: Micromachined capacitance transducers have been investigated in practical situations where air-coupled ultrasound has current application. Their /spl sim/2 MHz bandwidths lead to good performance in pulse-echo and through transmission operation at solid surfaces. Applications in surface profiling and distance measurement have been investigated. For the transduction of waves within solid media, the devices are shown to be capable of detecting longitudinal and shear waves at solid surfaces, as well as Rayleigh and Lamb waves. Examples are also given of fully noncontact, through transmission of carbon fibre reinforced polymer plates. >

Nonlinear Waves in Elastic Media

Abstract: Mathematical Introduction Conservation Laws and Related Differential Equations. Hyperbolic Systems. Linear and Linearized Equations. Riemann Invariants. Boundary Conditions and Evolutionary Properties. Riemann Waves. Discontinuities and Relations on Them. Shock Adiabat. Evolutionary Conditions for Discontinuity. Low Intensity Discontinuities. Shock Adiabat Behavior in a Vicinity of the Jouget Point. Conservation Law in the Godunov Form. Entropy. Entropy Production and Entropy Density Change on a Discontinuity. Solutions with Discontinuities as a Limit of Continuous Solutions to Equations of a Complicated Model. Small Perturbations in Dissipative Media. Shock Wave Structure. On Plane Wave Problems in Elastic Media Elastic Medium Model. Governing Equations. Plane Wave Equations. Conditions on a Discontinuity. Shock Adiabat. Entropy Change Along the Shock Adiabat. Wave Isotropy and Anisotropy. Internal Energy of a Medium with Weak Wave Anisotropy. Elastic Potential for a Weakly Nonlinear Medium. Nonlinear Wave Propagation Through Media Interacting with Electromagnetic Fields. Riemann Waves Small Perturbations. Linear Waves. Equations for Riemann Waves. Quasilongitudinal Waves. Quasitransverse Riemann Wave. Parameter Variations in Quasitransverse Waves. Evolution of Quasitransverse Riemann Waves. Riemann Waves in the Case of Wave Isotropy. Shock Waves Relationships on a Weak Shock Wave. Quasilongitudinal Shock Waves. Quasitransverse Waves. Shock Adiabat. Entropy Nondecreasing Condition. Evolutionary Conditions on Shocks. Velocities in Quasitranverse Waves. The Number of Evolutionary Shock Waves and Their Types. Locations of Evolutionary Segments on the Shock Adiabat. Shock Transitions into a Given State. Special Forms of Initial Deformations. Quasitransverse Shock Waves for G/R2

Elastic property measurement using Rayleigh-Lamb waves

Abstract: A nondestructive technique is described for the measurement of elastic constants of isotropic plates using ultrasonic Rayleigh-Lamb waves. The experimental method employs continuous harmonic waves and a pair of variable-angle contact transducers in pitch-catch mode. The phase velocity of the R-L waves at a particular frequency is determined from the phase shift over a measured path length. This simple experimental technique can measure phase velocity over the range 1–10 mm/µs with an error of less than 0.5% over a frequency range of 50 kHz-2 MHz. Individual symmetric and antisymmetric modes can be generated through the selection of transducer angle and frequency. Young's modulus and Poisson's ratio for the material are calculated from measurements of frequency and phase velocity by a nonlinear least squares solution to the dispersion equations. The sensitivity of the nonlinear least squares function to the measurement region of the dispersion curve is investigated. It was found that estimations of material properties are more accurate and less sensitive to small experimental errors when only selected frequencies and R-L modes are used in the least squares calculation. This technique is demonstrated with several isotropic materials and with both thick (6 mm) and thin (0.8 mm) plates. Values for elastic constants determined by the contact transducer Lamb wave technique compare favorably with values measured using the pulse-echo-overlap method. The uncertainty in measurements of Young's modulus and Poisson's ratio was less than 1% and 2%, respectively. The technique has advantages over more traditional methods for measuring elastic properties when it is desirable to use wavelengths greater than the plate thickness, when properties may vary with frequency, or when it is necessary to measure in-plane elastic properties of thin plate structures.

Ultrasonic Guided Waves For NDE of Adhesively Bonded Structures

Abstract: A rather sophisticated guided wave technology is introduced to solve a practical aging aircraft problem of delaminations and/or corrosion detection in either a lap splice joint or a tear strap. A Double Spring Hopping Probe is designed to achieve excellent contact on a curved aircraft structures. A guided wave resonance tuning concept for frequency is also discussed with respect to attaining reliable bond integrity measurements. A variety of experiments are discussed including experiments performed during the field trial on a Boeing 737-222 aircraft.

Interpretation of the band-structure results for elastic and acoustic waves by analogy with the LCAO approach.

Abstract: The band-structure results for elastic and acoustic waves propagating in a composite (consisting of periodically placed spheres in a host material) are analyzed by employing the frequency dependence of the scattering cross section from a single sphere. Two limiting modes of propagation can be visualized. According to the first the wave propagates mainly through the host material; according to the second the wave hops coherently from a sphere to its neighbors using the resonances in the single-sphere scattering cross section. This second mode is the analog of the linear combination of atomic orbitals in electronic propagation, with the atomic orbitals replaced by the resonances.

Magnetoelastic shear waves in an infinite self-reinforced plate

Abstract: The propagation of magnetoelastic shear waves in an infinite self-reinforced plate is studied in this paper. The frequency spectrum for SH-modes in the plate is drawn and it is shown that if the dimensionless wave number is real, the branches are hyperbolas while for imaginary wave numbers, they are ellipses. It is also observed that for higher modes, the dimensionless group velocity approaches 9·9754 as the wave number increases. The group velocity is normalized with respect to the phase velocity of shear waves. For a homogeneous and isotropic medium, on the other hand, the dimensionless group velocity approaches unity. So it is approximately 10 times larger in case of magnetoelastic shear waves in an infinite self-reinforced plate. It is also noted that in a reinforced medium, if both the values of the coupling parameter and the angle at which the wave crosses the primary magnetic field are increased, the values of the dimensionless frequency and group velocity are decreased.

Longitudinal guided wave propagation in a transversely isotropic rod immersed in fluid

Abstract: The propagation of longitudinal guided waves in fluid‐loaded transversely isotropic rods has been investigated based on the superposition of partial waves. The numerical results indicate that fluid loading causes not only significant attenuation via energy leakage into the fluid but also strongly affects the phase velocity of the modes in certain frequency ranges. There is an apparent ‘‘mode switching’’ between the two lowest‐order modes when the rod is loaded by a relatively high‐density fluid. This phenomenon is analogous to the anomalous topology previously observed in the Lamb wave spectra of low‐density water‐loaded plates.

On the completeness of Lamb modes

Abstract: A completeness result for Lamb modes in homogeneous waveguides is proved. The problem is formulated as a linear eigenvalue problem in an appropriate Hilbert space of functions. Orthogonality and biorthogonality relations are given. A detailed spectral analysis which is necessary for the application of a general completeness theorem is presented.

Comparison of Lamb waves and pulse echo in detection of near-surface defects in laminate plates

Abstract: One of the problems faced in ultrasonic nondestructive testing (NDT) of composite laminates is near-surface delaminations which may be due to impact damage. The normal incidence pulse echo technique has difficulty in resolving echoes from this type of defect since they often lie within the length of the transmitted ultrasonic pulse. Although a high frequency probe may be used, it has its limitations and could be problematic in composite materials in which ply reflections may interfere with defect reflections. The use of an acoustic delay, together with a high frequency probe, may improve the detection. In this paper, a different approach has been developed using the fundamental Lamb wave (S 0 mode) to detect delaminations in unidirectional fibre composite materials. It has been found that the Lamb wave amplitude decreases significantly over a delamination region. The decrease in amplitude is strongly dependent upon the depth of the delamination and is most sensitive to the delaminations near to the surface of the laminate. By scanning the transducer over the surface, it is possible to measure the size and depth of this kind of delamination. This technique is comparable to the delayed pulse echo technique and can be used to complement other techniques.

The propagation of lamb waves in a plate bordered with a viscous liquid

Abstract: The dispersion equations of Lamb waves of a plate bordered with a viscous liquid layer or half‐space viscous liquid on both sides have been derived. Numerical solutions of the dispersion equations related to sensing applications are presented.

AlN/silicon Lamb-wave microsensors for pressure and gravimetric measurements

Abstract: We have studied a pressure and a gravimetric sensor using an AlN film over a silicon membrane. The membrane is micromachine using both anisotropic and isotropic chemical etching. The AlN thin film is deposited by the sputtering method. Elastic waves are generated and detected through interdigital transducers (IDTs) calculated at the frequency of 90 MHz for the S 0 Lamb-wave mode. The behaviour of such a sensor is presented. We have analysed and experimentally tested the pressure and have calculated the gravimetric sensitivity. By using the opposite temperature behaviours of silicon and AlN, a satisfactory temperature compensation is achieved. Results obtained from such experiments show sensitivities that agree with theoretical sensitivities provided by a theoretical model which includes the effect of the mass loading of the deposited thin-layer material.

Surface Acoustic Wave Focusing and Induced Rayleigh Waves.

Abstract: We introduce a new method for observing the anisotropic propagation of surface acoustic waves on solids. Point source and point detection of ultrasonic waves, scanned as a function of propagation angle, give the group velocities and intensities of Rayleigh and pseudosurface waves. Group-velocity focusing and internal diffraction are observed for Si, and a new Rayleigh mode, induced by water loading of the surface, is discovered. Such effects are predicted for most anisotropic solids.

Determination of elastic constants of a concrete specimen using transient elastic waves

Abstract: This paper presents the results of measuring the Rayleigh wave as well as longitudinal wave velocities in a concrete specimen using transient elastic waves. The Rayleigh surface wave generated by a steel ball impact on a concrete material is studied in detail and then a method for the determination of Rayleigh surface wave velocity based on the cross‐correlation method is proposed. The longitudinal wave velocity of a concrete specimen is determined by measuring the wavefront arrival of a longitudinal wave. A special triggering device for the accurate determination of the impact time origin is utilized. The measured velocities of both the Rayleigh wave and the longitudinal wave in the concrete specimen are in good agreement with those measured by utilizing the conventional ultrasonic method. It is noted that with the Rayleigh wave and the longitudinal wave velocities measured, the Young’s modulus as well as the shear modulus of a concrete specimen can be obtained in a straightforward way.

Inspection of pipes

Abstract: An apparatus and a method for inspecting elongate members, especially pipes using Lamb waves. The apparatus and method provide for the propagation of an axi-symmetric Lamb wave of a single mode in one direction along the pipe. A means is provided to receive the Lamb wave after its passage along the pipe and convert the received wave for storage, processing and analysis to determine whether or not there are faults present in the pipe. The apparatus includes at least one and usually several excitation rings each comprising a plurality of Lamb wave exciters (5) deployed in equiangular spacing in a ring clamping means whereby each exciter can be pressed with equal force against the surface of the pipe under inspection.

Lamb Wave Tomography Using Laser-Based Ultrasonics

Abstract: Lamb waves are widely used for the nondestructive evaluation of plate structures. By using Lamb wave attenuation, velocity and mode conversion, information about the sizes and positions of existing defects can be obtained. Lamb waves have also been used for C-scan imaging of plates. In C-scan imaging, the measurement has to be performed at each point on the sample to characterize the material at that point. Recently, computed tomography techniques using Lamb waves and surface acoustic waves have been proposed and investigated [1–3]. The computed tomographic technique provides faster image reconstruction and the ability to image an area from outside the area. This is often desired when the defected area is not directly accessible.

In situ thin film thickness measurement with acoustic Lamb waves

Abstract: In situ thin film thickness measurement is an important problem in semiconductor processing, which is currently limited by the lack of adequate sensors. Most of today’s available techniques are restricted to certain type of films and many have difficulties in performing the measurement in situ. The fact that the velocity of an ultrasonic Lamb wave traveling in a silicon wafer is changed by the thin film coating on the wafer surface can be used as a monitoring method for basically any type of film—opaque, transparent, metal, or insulator. The acoustic sensors are easily implemented into plasma or CVD environments. We have demonstrated the technique in an aluminum sputtering system in which we measure Al film thickness with a resolution of ±100 A. Even better resolution can be achieved for SiO2, copper, and tungsten films. This system has a variety of potential applications, not only in film thickness measurement, but also in characterization of film properties and multilayer deposition process control.

Lamb wave tomography and its application in pipe erosion/corrosion monitoring

Abstract: Ultrasonic Lamb wave techniques are widely used in a number of NDE applications. To excite Lamb waves, mode conversion of bulk waves or photo acoustic excitation are often used. Both of these approaches suffer from the need for liquid couplant or ablation of materials to reach good signal to noise ratio. In this paper, we propose a novel technique that utilizes point source excitation and detection of Lamb waves through dry, elastic contacts to monitor velocity changes. We demonstrate the power of this approach in ultrasonic pipe erosion/corrosion monitoring and its potential application in aircraft skin defect imaging. We present results of measurements of plate thickness, and erosion/corrosion in a section of pipe that was removed from service, as well as imaging of defects in an aluminum thin plate.

Long non-linear strain waves in layered elastic half-space

Abstract: Elastic strain wave propagation in a thin non-linearly elastic layer superimposed on non-linearly elastic half-space is studied. Two layer-half-space contact models are considered. It is found that the Benjamin-Ono equation can be derived for description of longitudinal non-linear strain waves, when the contact between the layer and the half-space is provided only by means of the normal stresses and displacements. When the full contact problem is considered the more complicated integro-differential equation is derived. It is found that long non-linear periodical and solitary strain waves as well as envelope waves may exist in the first case, while only envelope wave solutions are found to the full contact problem. Linear wave analysis shows that the Korteveg-de Vries equation, often usable, is unlikely to be an adequate model for longitudinal surface strain waves. Application of the results obtained to experiments devoted to superconductivity threshold control in thin metal films as well as to generation of acoustic solitons in layered half-space is discussed.

Identifying source of acoustic emissions in structures using lamb waves and vibration modes

Abstract: A process for global monitoring of a structure for location of a source of acoustic emissions using the vibration modes of a structure together with the repetition rate of acoustic emission events in said structure thereby allowing determination of source location of acoustic emission events in said structure is provided. Further a process for identifying the arrival of different modes of lamb waves at the same transducer distance, based on the different propagation velocities of these modes is also provided so as to determine the distance from a single transducer to the source of said lamb waves.

The instability of internal gravity waves to localised disturbances

Abstract: The instability of an internal gravity wave due to nonlinear wave-wave interaction is studied theoretically and numerically. Three different aspects of this phenomenon are examined. 1. The influence of dissipation on both the resonant and the nonresonant interactions is analysed using a normal mode expansion of the basic equations. In particular, the modifications induced in the interaction domain are calculated and as a result some modes are shown to be destabilised by dissipation. 2. The evolution of an initial unstable disturbance of finite vertical extent is described as the growth of two secondary wave packets travelling at the same group velocity. A quasi-linear correction to the basic primary wave is calculated, corresponding to a localised amplitude decrease due to the disturbance growth. 3. Numerical experiments are carried out to study the effect of a basic shear on wave instability. It appears that the growing secondary waves can have a frequency larger than that of the primary wave, provided that the shear is sufficient. The instability of waves with large amplitude and long period, such as tides or planetary waves, could therefore be invoked as a possible mechanism for the generation of gravity waves with shorter period in the middle atmosphere.

Backscattering near the coincidence frequency of a thin cylindrical shell: Surface wave properties from elasticity theory and an approximate ray synthesis

Abstract: A simple ray approximation is demonstrated for the backscattering of sound by a thin empty cylindrical shell in water at normal incidence. The approximation is applied to the region near the coincidence frequency and is used to interpret prominent features in that region associated with a subsonic guided wave. With increasing ka, the features exhibit a transition from resonance behavior dominated by interference with the specular reflection. Another feature is the interference of resonance contributions of the leaky s0 Lamb wave which may produce maxima or minima in the amplitude depending on the ka region. The cylinder studied is 2.5% thick stainless steel for ease of comparison with a similar spherical shell [P. L. Marston and N. H. Sun, J. Acoust. Soc. Am. 92, 3315–3319 (1992)] and the guided wave properties were computed from elasticity theory rather than shell approximations. A novel geometric derivation is given for the relative phases of the coupling coefficients of subsonic waves on cylinders and ...

Three-wave coupling in the auroral E-region : Progress in understanding ionospheric irregularities

Abstract: Analysis of a simple model for two-stream weak fluid turbulence suggests a straightforward mechanism for the excitation of plasma wave modes whose phase velocities are roughly half the ion-acoustic speed. This slow wave is linearly stable but is excited through three-wave interaction with two other waves, at least one of which is an unstable two-stream wave. All three waves satisfy the linear dispersion relation. Careful consideration of the coupling coefficients and resonance conditions shows that the driven (linearly stable) modes have k-vectors that are perpendicular to the local magnetic field and are perpendicular to the local magnetic field and are at some large angle to the Hall drift direction . These waves have phase velocicities in the neighborhood of half the ion-acoustic speed and they could be responsible for type-3 radar echoes observed at 50 MHz. This mechanism cannot, however, generate fast waves moving at type-4 velocities

Imaging of surface acoustic waves

Abstract: A new experimental method has been devised that directly determines the group velocities of surface acoustic waves. A point source and a point detector are employed to measure the ultrasonic transmission across a solid surface as a continuous function of the propagation direction. Results for single pulses give the times-of-flight for both Rayleigh surface waves (RSW's) and pseudo-surface-waves (PSW's). Calculations and measurements of the group velocities of the surface waves on silicon show some unanticipated behavior: fluid loading qualitiatively changes the group velocity curves for both RSW and PSW. In particular, the RSW branch gains an additional component which we denote here as an induced Rayleigh wave (IRW). If a wave train is employed in the experiment, the analog of phonon focusing is observed for the ultrasonic waves, modified by “internal-diffraction” effects. Systematic measurements of the wave intensities on silicon as a function of propagation distance are consistent with expected acoustic losses into the surrounding water: the attenuation length of a wave depends on the mode and frequency. A survey of surface-wave images on other crystals is included in this study.

Improved boundary conditions to a time-dependent mild-slope equation for random waves

Abstract: The offshore and side boundary conditions to a, time-dependent mild slope equation for random waves are improved to introduce given incident waves into and extract reflected waves from the computational domain with reduced computational time and storage size. The resulting numerical model is applied to calculate the wave field, nearshore current, and bottom topography change around a detached breakwater.