Plate Wave Modes Research Articles

Ultrawide-Band Resonators Using Shear Horizontal-Type Plate Wave and Their Application

Currently, mobile or smart phones with multibands and a cognitive radio system require a tunable filter with a wide tunable range to simplify their circuits. An ultrawide-band resonator is an important device to realize the tunable filter. The relative bandwidths (BWs) of 12 to 17% of previously reported surface acoustic wave (SAW) resonators are not sufficient to realize the tunable filter. This time, the authors studied an SH0 mode plate wave in a LiNbO3 plate. As a result, plate wave resonators with a large electro-mechanical coupling factor (k2) of 0.55 (55%), an ultrawide bandwidth of 29%, a high Q of 700, and a large impedance ratio of 98 dB between resonance (fr) and anti-resonance (fa) frequencies were realized for the first time using 27.5–30°YX-LiNbO3 plates. Applying these resonators to a ladder-type tunable filter, a wide tunable range of 19% was obtained.

Acoustic Emission Source Characterisation in Large-Scale Composite Structures

Damage detection and location in aerospace composites is currently of great interest in the research community and is being driven by the need to reduce weight of commercial aircrafts and hence make substantial environmental improvements. The increased use of composites as safety critical components has led to the need for development of structural health monitoring (SHM) systems. Acoustic Emission (AE) offers an excellent potential for delivering the necessary information of damage detection to maintenance engineers in terms of location however there are currently no methodologies that can use AE signals to characterise damage sources. This paper explores a methodology for damage characterisation based on measuring the amplitude ratio (MAR) of the two primary plate wave modes, to allow identification of in-plane (matrix cracking) and out-of-plane sources (delamination). Results from a large-scale buckling test show good correlation between signal characterization and observed damage mechanisms.

A hybrid finite element model for simulation of electromagnetic acoustic transducer (EMAT) based plate waves

This paper reports simulations of the generation of Lamb wave modes in thin plates using a meander coil (meander line) EMAT, which works under the principle of Lorentz force mechanism in non-magnetic materials. The numerical simulations have been compared with measurements. The numerical work presented in this paper is divided into two parts. First, a 2D electromagnetic model is developed for calculating the Lorentz force density, which is the driving force for elastic wave generation within the plate. Second, the calculated force at each point in the metal is used as the driving force for generating elastic wave modes in the plate. These calculated Lamb wave modes are compared with those generated experimentally in a thin plate. Additionally, the measured wave modes are analyzed with the help of dispersion curves and a time–frequency analysis. Our numerical work is also extended to analyze the interaction of Lamb wave modes with defects. The simulations compare favorably with the measurements presented here.

An investigation of vibration-induced protein desorption mechanism using a micromachined membrane and PZT plate

A micromachined vibrating membrane is used to remove adsorbed proteins on a surface. A lead zirconate titanate (PZT) composite (3 x 1 x 0.5 mm) is attached to a silicon membrane (2,000 x 500 x 3 microm) and vibrates in a flexural plate wave (FPW) mode with wavelength of 4,000/3 microm at a resonant frequency of 308 kHz. The surface charge on the membrane and fluid shear stress contribute in minimizing the protein adsorption on the SiO(2) surface. In vitro characterization shows that 57 +/- 10% of the adsorbed bovine serum albumin (BSA), 47 +/- 13% of the immunoglobulin G (IgG), and 55.3~59.2 +/- 8% of the proteins from blood plasma are effectively removed from the vibrating surface. A simulation study of the vibration-frequency spectrum and vibrating amplitude distribution matches well with the experimental data. Potentially, a microelectromechanical system (MEMS)-based vibrating membrane could be the tool to minimize biofouling of in vivo MEMS devices.

Magnetostrictive Sensor for Generating and Detecting Plate Guided Waves

The development of a magnetostrictive sensor for generating and detecting guided waves in ferromagnetic plate is described. The sensor consists of a channel-shaped core and coils wound around the core along its length. It is shown that the sensor is capable of generating and detecting both the symmetric and antisymmetric Lamb wave modes and the shear horizontal wave modes in plates. It is also found that the beam pattern produced by the sensor follows the pattern expected for a line source in a two-dimensional medium.

Dynamic holographic imaging of acoustic motion

Optical measurement of acoustic motion at a surface is usually accomplished with a scanning point probe. A full-field view acoustic imaging microscope is described that records subnanometer displacement amplitude and phase over a surface without scanning. Images are recorded at video frame rates and heterodyne principles are used to allow operation at any frequency from Hz to GHz. Fourier transformation of the acoustic displacement image provides a mapping of excited mode wavenumbers at any frequency. This method readily measures (a) the acoustic displacement of transducers, (b) acoustic bulk wave reflection from subsurface objects in solids and liquids, (c) resonant ultrasound vibration modes of complex shapes, (d) surface acoustic waves, and (e) plate wave modes in isotropic and anisotropic materials. These and other examples are presented along with discussion and analysis for characterizing material properties, such as physical dimensions, material elastic properties, crystal orientation, electromechanical coupling, and the identification and visualization of defects.

High contrast air-coupled acoustic imaging with zero group velocity lamb modes

The well known zero in the group velocity of the first-order symmetric (S 1) plate wave mode has been exploited in air-coupled ultrasonic imaging to obtain significantly higher sensitivity than can be achieved in conventional air-coupled scanning. At the zero group velocity point at the frequency minimum of the S 1 mode, a broad range of wavenumbers couple into the first-order symmetric mode at nearly a constant frequency, greatly enhancing transmission at that frequency. Coupled energy remains localized near the coupling point because the group velocity is zero. We excite the mode with a broadband, focussing, air-coupled transducer at the frequency of the zero group velocity point in the S 1 mode. By exploiting the efficient coupling at the zero group velocity frequency, we have easily imaged a single layer of Scotch tape attached to a 6.4-mm thick Plexiglas plate and 3.2-mm Teflon inserts in a composite laminate.

Radiation efficiency analysis of submillimeter‐wave receivers based on a modified spectral domain integration technique

Reflector backed submillimeter‐wave slot antennas on substrate lenses are promising candidates for novel astronomical applications in integrated receivers for the far infrared region. Using an adjustable reflector, considerable resonance frequency tuning can be achieved, but with the risk of exciting parasitic parallel plate wave modes. Employing a surface/volume integral equation method and advanced spectral domain integration techniques, a complete radiation efficiency analysis of such kind of receivers is performed. Convenient integration path deformations in complex wavenumber planes allow a very fast evaluation of the spectral domain integrals in combination with efficient database and asymptotic extraction techniques. Saddle point and residue calculation techniques are employed to accurately determine the power of each parallel plate mode and the space wave contributions. The simulations reveal an appropriate set of parameters reducing the radiation loss to less than 10 percent for doubleslot and quadratic slot geometries preserving high tuning capability and optimized radiation patterns as well.

Off-axis propagation of ultrasonic guided waves in thin orthotropic layers: theoretical analysis and dynamic holographic imaging measurement.

The elastic properties of many materials in sheet or plate form can be approximated with orthotropic symmetry. In many sheet material manufacturing industries (e.g., the paper industry), manufacturers desire knowledge of certain anisotropic elastic properties in the sheet for handling and quality issues. Ultrasonic wave propagation in plate materials forms a method to determine the anisotropic elastic properties in a nondestructive manner. This work explores exact and approximate analysis methods of ultrasonic guided wave propagation in thin layers, explicitly dealing with orthotropic symmetry and propagation off-axis with respect to the manufacturing direction. Recent advances in full-field ultrasonic imaging methods, based on dynamic holography, allow simultaneous measurement of the plate wave motion in all planar directions within a single image. Results from this laser ultrasonic imaging approach are presented that record the lowest anti-symmetric (flexural) mode wavefront in a single image without scanning. Specific numerical predictions for flexural wave propagation in two distinctly different types of paper are presented and compared with direct imaging measurements. Very good agreement is obtained for the lowest anti-symmetric plate mode using paper properties independently determined by a third party. Complete determination of the elastic modulus tensor for orthotropic layers requires measurement of other modes in addition to the lowest anti-symmetric. Theoretical predictions are presented for other guided wave modes [extensional (S), flexural (A), and shear-horizontal (SH)] in orthotropic plates with emphasis on propagation in all planar directions. It is shown that there are significant changes in the dispersion characterization of these modes at certain frequencies (including off-axis mode coupling) that can be exploited to measure additional in-plane elastic moduli of thin layers. At present, the sensitivity of the imaging measurement approach limits experimental investigation to relatively large amplitudes easily produced by flexural wave motion (> 0.1 nm). Extension of the measurement range and application to other plate wave modes are in progress and shall be reported in future work.

Scattering of guided SH-wave by a partly debonded circular cylinder in a traction free plate

A solution of the scattering problem of guided SH-wave by a partly debonded circular cylinder centered in a traction free plate has been set up. The plate is divided up into three regions with two imaginary planes perpendicular to the plate walls. In the central region where the partly debonded cylindrical obstacle is posted, the wave field is expanded into the cylindrical wave modes and Chebyshev polynomials. In the other two exterior regions the fields are expanded into the plate wave modes. A system of fundamental equations to solve the problem is obtained according to the traction free boundary condition on the plate walls and the continuity condition of the traction and the displacement across the imaginary planes. The approximate numerical method termed mode-matching technique is used to construct a matrix equation to obtain curves showing the coefficient of reflection and transmission versus the ratio of the cylinder’s radius to the plate’s half-thickness and the angular width of the debonded region. A comparison of the numerical results between the welded interface condition and the debonded interface condition is made, and the results are discussed.

Scattering of antiplane shear waves by a circular cylinder in a traction-free plate

Following a well-established formula used by many researchers, the scattering of an anti-plane shear wave by an infinite elastic cylinder of arbitrary relative radius centered in a traction-free two-dimensional isotropic plate has been examined. The plate is divided into three regions by introducing two imaginary planes located symmetrically away from the surface of the cylinder and perpendicular to surfaces of the plate. The wave field is expanded into cylinder wave modes in the central bounded region containing the cylinder, while the fields in the other two outer regions are expanded into plate wave modes. A system of equations determining the expansion coefficients is obtained according to the traction-free boundary conditions on the plate walls and the stress and displacement continuity conditions across the imaginary planes. By taking an appropriate finite number of terms of the infinite expansion series and a few selected points on the two properly chosen virtual planes and the surfaces of the plate through convergence and precision tests, a matrix equation to numerically evaluate the expansion coefficients is found. The method of how to choose the locations of the imaginary planes and the terms of the expansion series as well as the points on each respective boundary is given in Sec. III in detail. Curves of the reflection and transmission coefficients against the relative radius of the cylinder in welded and slip or cracked interfacial conditions are shown. Analysis on the contrast variations of the reflection and transmission coefficients for a cylinder in bonded and debonded interfacial situations is made. The relative errors estimated by the deviation of the numerical results from the principle of the conservation of energy are found to be less than 2%.

Contactless measurement of the elastic Young's modulus of paper by an ultrasonic technique

The use of a non-contact ultrasonic technique for the characterization of the in-plane elastic Young's moduli of paper is considered. The determination of these moduli from A 0 (fundamental antisymmetric plate wave mode) measurements, using the empirical technique introduced by Luukkala et al. (1971), is discussed: it is shown that the common low frequency approximation is not valid for paper, owing to its orthotropic structure. Numerical simulations are used to evaluate the validity domain of Luukkala's method. A new device was developed, and Young's moduli of various paper sheets were determined from A 0 measurements. These moduli values were found to be in good agreement with those measured using a common laboratory contact ultrasonic technique.

Acoustic plate waves in potassium niobate singlecrystal

The characteristics of acoustic waves propagating in thin plates of single crystal potassium niobate (KNbO3) have been theoretically investigated. It is found that acoustic plate wave modes can provide much stronger electromechanical coupling (ΔV/V = 0.51) than is possible with surface acoustic waves (ΔV/V = 0.265).

Fluid-borne and Lamb-type waves on elastic plates in contact with two different fluids

The subject of propagating waves on fluid-loaded plates and shells, and their acoustic excitation, has become of great current interest. Besides the existence of the Lamb-type plate or shell wave modes, a water-borne Scholte-Stoneley wave has been found on plates or shells specifically with one-sided water loading. Another specific case is that with two-sided water (or same-fluid) loading; here a symmetrical Scholte-Stoneley wave was found in addition to an antisymmetric one. In this paper, more generally, the plate loaded with two different fluids is discussed via the corresponding dispersion curves of plate and fluid-borne waves. The existence of two Scholte-Stoneley waves has been confirmed for this case.

Two Scholte–Stoneley waves on doubly fluid-loaded plates and shells

Previous theoretical and experimental studies of sound scattering from plates and from evacuated cylindrical or spherical shells with one-sided water loading have demonstrated the existence of a water-borne Scholte–Stoneley wave, and its acoustic excitation, in addition to that of the Lamb-type plate or shell wave modes. For two-sided water loading two Scholte–Stoneley waves, of symmetric (S) and antisymmetric (A) nature, were predicted on plates, with only the A wave surviving for the case of one-sided loading, while for loading with two different fluids, again two such waves have been demonstrated theoretically. In the present investigation, these two Scholte–Stoneley waves are studied experimentally via short-pulse scattering from water-immersed, thin-walled cylindrical shells filled alternatingly with air, water, and alcohol, and a theoretical analysis of their dispersion curves is presented.

Driving mechanism on magnetostrictive type electromagnetic acoustic transducer for symmetrical vertical-mode Lamb wave and for shear horizontal-mode plate wave

The properties of electromagnetic acoustic transducers (EMATs) for using the symmetrical vertical mode-(S0) Lamb wave and the shear horizontal fundamental mode-(SH0) plate wave were experimentally studied. The EMAT, consisting of a meandering coil and an electromagnet, can effectively transmit and receive the S0 mode Lamb wave and the SH0-mode plate wave in a thin metal plate. For ferromagnetic materials, such as steels, the magnetostriction is important for the transduction. The wave amplitude is not proportional to the static field strength, but is dependent on the magnetostrictive properties of the material. In this study, the amplitude and the phase of the S0 mode Lamb wave and SH0 mode plate wave generated by the EMATs are measured while changing the static field strength to the sheets. The amplitude of the S0-mode Lamb wave in a low carbon steel sheet initially decreases with a static field to the minimum value, then increases again accompanying the phase inversion by 180 ° and finally decreases without any phase inversion. The amplitude of the SH0 mode plate wave in a low carbon steel sheet initially increases to the maximum value with the static field, then decreases to the minumum value and increases again accompanied by a phase inversion of about 90 °. These data were discussed on the basis of the magnetostrictive curve to the magnetizing current of an electromagnet in low carbon steel sheets.

Single mode Lamb wave excitation in thin plates by Hertzian contacts

We present novel techniques to selectively excite the lowest order symmetric (So) and antisymmetric (Ao) Lamb wave modes in thin solid plates. Hertzian contacts are formed between the plates and the end of specially designed quartz rods which guide extensional waves generated by PZT-5H transducers bonded at their other end. Mode selectivity is achieved by applying shear and/or longitudinal traction at the edge or the surface of the plates according to the results of a two-dimensional normal mode theory. In aluminum plates, mode selectivity is measured as a function of frequency for different traction forces. With normal forces, Ao mode selectivity of more than 46 dB is obtained for fd<0.4 MHz mm. With antisymmetric shear traction at the edge of the plate, a selectivity exceeding 55 dB is achieved for single mode So operation.

Hertzian contact transducers for nondestructive evaluation

Hertzian, dry, pointlike contacts are used to couple ultrasonic energy efficiently to plate wave modes in anisotropic solid plates. A new transducer configuration using a piezoelectric PZT-5H transducer and a quartz buffer rod is realized for this purpose. In particular, the lowest order antisymmetric Lamb wave (A0) mode is excited and detected in anisotropic plates at a frequency of 200 kHz and with signal-to-noise levels exceeding 65 dB. Time delay measurements and FFT techniques are used to obtain dispersion and anisotropy curves of phase velocity in anisotropic plates. The accuracy of the method is limited mainly by the distance measurements. In (001) silicon plates the agreement between theory and experiments is obtained with an accuracy of ±0.08%. Anisotropic phase velocity measurements are also performed for uniaxial graphite/epoxy composite plates and the results are compared with the theoretical model to derive the elastic constants of the composite. Through accurate phase velocity measurements, it is possible to detect delamination defects in composite plates with high resolution operating at 200 kHz. Using the surface impedance approach, a model is also developed to predict the effects of delaminations on phase velocity and the results are verified by experiments.

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.

Transverse and plate waves for adhesive bond interface evaluation: Proceedings of the 12th World Conference on non-destructive testing, Amsterdam (Netherlands) 23–28 Apr. 1989, vol. 1, pp. 836–841. Edited by J. Boogard and G.M. van Dijk, Elsevier, 1989

SUMMARY Two approaches for detection of interfacial weakness between an adhesive and adherend are proposed here. The first technique employs transverse waves at an angle of incidence chosen from numerically established angular characteristics of the reflection factor in the case of two elastic media connected by different boundary conditions. A comparison of experimental and theoretical results confirms the importance of frequency and angle selection. The second approach discussed here is based on plate wave behavior in three layered medium with imperfections on the individual interfaces. A selection of appropriate modes was obtained indirectly by a numerical analysis of the dispersion relations. The different degrees of sensitivity of the individual plate wave modes either to interfacial conditions or to changes in glue line thickness and its cohesive properties was underline.