Plate Acoustic Waves Research Articles

Micromachined thin film plate acoustic wave resonators (FPAR): Part II

Improved performance thin-film plate acoustic wave resonators (FPAR) using the lowest order symmetric Lamb wave (S0) propagating in highly textured AlN membranes have been previously demonstrated for the first time. In this work, an experimental study of the resonators' performance vs. a variety of design parameters is performed. Devices operating in the vicinity of the stopband center exhibiting a Q-value of up to 3000 at a frequency of around 875 MHz are demonstrated. Further, low-loss high-Q micromachined 2-port longitudinally coupled thin-film resonators using the S0 mode are demonstrated for the first time. For the analysis of the proposed structures, the coupling-of-modes (COM) approach is successfully employed. Initially, the COM model is used for the extraction of physical parameters from one-port FPAR measurements. Subsequently, using the COM model, a satisfactory agreement with the proposed experimental frequency characteristics of S0 2-port FPARs has been achieved, and possibilities for further improvements in the performance discussed. Finally, the frequency spectrum of the one-port devices has been studied and the excited plate modes at different frequencies identified and presented with their Q-factors and temperature coefficients of frequency (TCF).

Theoretical and experimental study of plate acoustic waves in ZX-cut lithium niobate

In this work, we report theoretical and experimental results on the 8 lowest modes of plate acoustic waves (PAW) propagating along the x-axis in the Z-cut of LiNbO3 wafers (the ZX-cut). Dispersion curves are calculated by the method of partial waves and by the Finite Element Method (FEM); the curves are then measured experimentally. The spectra obtained by the 2 methods are in good agreement with each other and with the experimental results. The PAW modes are identified as components of the total acoustic displacements near cutoff frequencies. Electromechanical coupling efficiency of the 8 modes is described. The FEM work is verified by an application to the design and testing of a PAW delay line in a ZX-cut LiNbO3 wafer. These results may be useful for analysis of many devices fabricated in Z-cut wafers, such as acoustoelectric and acousto-optic components, ultrasonic motors and actuators, micro/nano-particle transporters, and other devices employing periodically poled ferroelectric waveguides.

Dispersion of plate acoustic waves in periodically poled lithium niobate.

The phase and group velocity dispersion of the plate acoustic waves (PAWs) in ZX-cut periodically poled lithium niobate (PPLN) wafer is calculated theoretically and verified experimentally. The dispersion curves of eight lowest PAW modes are calculated with the help of the finite element method. The PAWs in PPLN have some peculiarities in comparison with the case of a single crystal waveguide. First, some PAW modes may reflect out of the multidomain structure, and so a band gap may occur in the PAW spectrum. For example, a zero antisymmetric mode A0 has 0.2-MHz-wide band gap at frequency where its wavelength is equal to the period of a domain pattern. Second effect includes a variation of a cutoff frequency of PAW. The experimental dispersion curves are in agreement with calculations. The phononic band gap of A0 mode and the cutoff frequency shift of first antisymmetric mode A1 are confirmed by our experiments. The group velocity is calculated from the experimental phase-velocity dispersion curves. The calculated and measured group velocities are consistent. It is shown that the group velocity of A0 mode approaches zero within the band gap.

Phononic band gaps in periodically corrugated lithium niobate plate.

A ZX-cut lithium niobate crystalline plate with a periodic corrugation is shown to have the band gaps in its spectrum of the plate acoustic waves. The corrugated plate is modeled numerically using finite element method. The depth of corrugations is 20% of the plate thickness along the Z-axis, and the corrugation period along the X-axis is taken from 0.3 to 1 mm for different model samples. The phase and group velocities of propagating acoustic modes will be affected significantly by the periodic change of plate thickness. The cutoff frequencies of higher-order modes will increase, and some new plate acoustic waves will appear. The periodic corrugations will cause the reflections and band gaps in the spectra of propagating modes. The strongest effects occur when the period of corrugations is equal to an integer number of half wavelengths of a mode. However, the distortions of the spectra do not appear in the spectrum if only 10% of the plate length is corrugated. One can achieve a complete band gap with certain corrugation periods and plate thicknesses. A periodically poled corrugated LiNbO3 is also considered. These acoustic properties of a phononic LiNbO3 crystal may be employed in a new generation of acoustic filters.

The power flow angle of acoustic waves in thin piezoelectric plates

The curves of slowness and power flow angle (PFA) of quasi-antisymmetric (A(0)) and quasi-symmetric (S(0)) Lamb waves as well as quasi-shear-horizontal (SH(0)) acoustic waves in thin plates of lithium niobate and potassium niobate of X-,Y-, and Z-cuts for various propagation directions and the influence of electrical shorting of one plate surface on these curves and PFA have been theoretically investigated. It has been found that the group velocity of such waves does not coincide with the phase velocity for the most directions of propagation. It has been also shown that S(0) and SH(0) wave are characterized by record high values of PFA and its change due to electrical shorting of the plate surface in comparison with surface and bulk acoustic waves in the same material. The most interesting results have been verified by experiment. As a whole, the results obtained may be useful for development of various devices for signal processing, for example, electrically controlled acoustic switchers.

The peculiarities of propagation of the backward acoustic waves in piezoelectric plates

The characteristics of backward acoustic waves in piezoelectric plates under different electrical boundary conditions were investigated. It has been shown that electrical shorting of the plate leads to increasing and decreasing the phase velocity for backward and forward branches, respectively. The peculiarities of the hybridization effect of backward waves were studied.

Miniature, high efficiency transducers for ultrasonic flow meter applications

This paper is concerned with the development of novel, miniature, high efficiency transducers for use in ultrasonic flow meters. Theoretical and experimental work done in our laboratory has shown that a flat, planar transducer that has minimal protrusion into the flow pipe can be realized based on conversion of plate acoustic waves (PAWs) to bulk acoustic waves (BAWs) and vice versa. The transducer is essentially a thin plate of a suitable piezoelectric material on which intedigital transducers (IDTs) are fabricated to generate and detect plate acoustic waves. With proper design very efficient conversion of energy from plate waves in the piezoelectric material to bulk waves in the fluid (and vice versa) can be achieved. For example, using lithium niobate as the piezoelectric material and water as the fluid, total conversion loss (PAW to BAW and back from BAW to PAW) of less than 2.5 dB has been obtained. An important advantage of plate waves is that since wave energy is present on both plate surfaces, the IDT can be on the surface opposite from that which is in contact with the fluid. Details of the theoretical analysis used, experimental results obtained, and potential applications will be presented.

Characterization of stiffness degradation caused by fatigue damage in textile composites using circumferential plate acoustic waves

The aim of this paper is to show the possibility of fatigue damage characterization in GFRP-tube-like components by using circumferential plate waves. For that purpose, fatigue tests with different loading directions have been conducted and the stiffness degradation has been monitored. After a preset number of loading cycles, non-destructive ultrasonic tests using circumferential plate waves were performed. The correlation between damage induced amplitude changes of the plate waves and stiffness degradation in non-crimped fabric composites is discussed. The results indicate that the technique is applicable to fatigue damage assessment in complex-shaped components of composite materials and is relevant to a wide field of applications.

Hybridization of backward acoustic waves in piezoelectric plates

The phenomenon of hybridization of the backward acoustic waves propagating in a piezoelectric crystal plate has been studied. In an electrically free plate (in particular, of potassium niobate) with a crystal orientation for which a sagittal plane is the symmetry plane, the dispersion curves of backward acoustic waves exhibit points of intersection and hybridization is absent. However, for a small change in the direction of wave propagation, the dispersion curves exhibit “repulsion” and the waves become coupled. The degree of hybridization is quantitatively evaluated in terms of the hybridization coefficient, which is defined as the ratio of the total mutual energy density and the total energy density of the interacting waves. It is demonstrated that the extent of repulsion of the dispersion curves for the interacting waves is determined by the dependence of the hybridization coefficient on the product of the plate thickness and the wave frequency.

Integrated piezoelectric plate acoustic waves transducers

A piezoelectric film has been fabricated by a sol-gel spray technique directly onto an edge of a 2 mm-thick aluminium plate as an integrated ultrasonic transducer and used to detect line defects at a distance using mode converted symmetric and shear horizontal waves at 150°C.

Laser-generated thermoelastic acoustic sources and Lamb waves in anisotropic plates

The effect of anisotropy and temperature on the dispersive Lamb wave generation and propagation in a transversely isotropic thin plate has been investigated. A quantitative numerical model for the laser-generated transient ultrasonic Lamb waves propagating along arbitrary directions is presented by using a finite-element method. All factors, such as spatial and time distributions of the incident laser beam, optical penetration, thermal diffusivity, thickness of the plate, and source–receiver distance, can be taken into account. The effects on the ultrasound waveform of the size of the optoacoustic source are investigated; in the limit of strong optical absorption, a subsurface thermal source gives rise to both vertical and lateral shear tensions. The lateral shear tension is equivalent to applying a shear dipole at the top face; the amplitude of the dipole is a function of material symmetry, contrary to the isotropic case, and the character and strength of the equivalent surface stress are a function of propagation direction. The specific results for the lower anti-symmetric and symmetric mode propagation in all planar directions are presented in the thermoelastic regime; the spatial dispersion (variation of the velocity with the direction of propagation) as well as the frequency dispersion is analyzed.

A two-dimensional analysis of surface acoustic waves in finite elastic plates with eigensolutions

It is generally known that surface acoustic waves, or Rayleigh waves, have different mode shapes in infinite plates. To be precise, there are both exponentially decaying and growing components in plates appearing in pairs, representing symmetric and antisymmentric modes in a plate. As the plate thickness increases, the combined modes will approach the Rayleigh mode in a semi-infinite solid, exhibiting surface acoustic wave deformation and velocity. In this study, the two-dimensional theory for surface acoustic waves in finite plates is extended to include the exponentially growing modes in the expansion function. With these extra equations, we study the surface acoustic waves in a plate with different thickness to examine the coupling of the exponentially decaying and growing modes. It is found that for small thickness, the two groups of waves are strongly coupled, showing the significance of including the effect of thickness in analysis. As the thickness increases to certain values, such as more than five wavelengths, the exponentially decaying modes alone will be able to predict vibrations of surface acoustic wave modes accurately, thus simplifying the equations and solutions significantly.

Propagation of acoustic waves in phononic-crystal plates and waveguides using a finite-difference time-domain method

Propagation of acoustic waves in a phononic-crystal plate and related waveguides are analyzed in this paper. A two-dimensional phononic-crystal plate consisting of circular steel cylinders which form a square lattice in an epoxy matrix is studied first using the finite-difference time-domain (FDTD) method. The Bloch theorem is employed to deal with the periodic condition, and the traction free condition is set on the top and bottom boundaries of the plates. The dispersion curves and displacement fields are calculated to identify the band gaps and eigenmodes. With the existence of a complete band gap in the phononic-crystal plate, an acoustic waveguide is presented accordingly. Eigenmodes of acoustic waves inside the waveguides are indicated, and the modes are affected by the geometry arrangement of waveguides. Inside the phononic-crystal plate waveguides, wave propagation is well confined within the structure.

Integrated High-Temperature Longitudinal, Shear, and Plate Acoustic-Wave Transducers

Thick (>40 µm) piezoelectric ceramic films were deposited on metallic substrates by a spray technique to fabricate shear (S) wave probes, longitudinal and shear (L&S) wave probes, and plate acoustic-wave (PAW) transducers for nondestructive testing and characterization (NDT&C) at elevated temperatures. Integrated ultrasonic S-wave probes were fabricated onto a steel substrate with the use of a mode conversion method from L-waves to S-waves. Probes that can simultaneously generate and receive both L- and S-waves were also developed. They operated at up to 350 °C with a center frequency of 5–7 MHz, a 6 dB bandwidth of 4–6 MHz, and a signal-to-noise ratio (SNR) of more than 20 dB. In addition, the fabrication and ultrasonic performance of integrated PAW transducers directly fabricated onto stainless-steel (SS) plates for NDT&C applications have been performed. Theoretical calculations and experimental results indicate PAW propagation in the first antisymmetrical mode along the 0.702-mm-thick SS plate. The PAW signals observed with good SNR demonstrate the NDT&C capability of these integrated PAW transducers in a distance of 5–60 cm operated at 350 °C.

Hybridization of acoustic waves in piezoelectric plates

The interaction (hybridization) of different types of acoustic waves of zero and higher orders propagating in lithium niobate piezoelectric plates is theoretically investigated. Different crystallographic orientations of the plates and different directions of wave propagation in them are considered. It is shown that, for an electrically free plate with the propagation direction along any of the crystallographic axes, the dispersion curves have intersection points and hybridization is absent. However, when the propagation direction slightly changes or when one of the plate surfaces is short-circuited, the dispersion curves separate and the waves become coupled. A quantitative coefficient characterizing the degree of wave hybridization with allowance for both mechanical and electric coupling is introduced. It is shown that the dependence of this coefficient on the product of the plate thickness by the wave frequency determines the extent of separation of the dispersion curves of interacting waves. The phenomenon under study is of both fundamental and practical interest, for example, in connection with the problem of an efficient excitation of nonpiezoactive acoustic waves in piezoelectric plates.

Thickness-Twist Edge Modes in a Semi-Infinite Piezoelectric Plate of Crystals with 6mm Symmetry (Letters)

It is shown that simple and exact thickness-twist edge modes exist in a semi-infinite piezoelectric plate of crystals with 6mm symmetry. This suggests the possibility of new thickness-twist plate edge mode resonators and acoustic wave sensors with certain advantages.

Generation of narrowband antisymmetric lamb waves using a formed laser source in the ablative regime

A formed laser source, using a four-element lenticular array, is used in the ablative regime to generate select, narrowband, acoustic plate waves. The arrangement of the array produces acoustical signals that have frequencies compatible with the response of the broadband capacitive air-coupled transducer used in this study. A simplified concept is presented to explain the effect of a line array source on the frequency content of acoustic waves. The analytical model for a point pulse surface displacement is derived from the point load solution to Lamb's problem. The point pulse displacement elements of a line array source are summed mathematically, taking into account all applicable propagation modes and dispersion of plate waves. The model considers only the out-of-plane displacement of the antisymmetric plate modes to represent the detection capability of the broadband receiver. The distribution function of the laser beam energy profile is modified to depict the actual energy distribution that illuminates the surface of the plate. Filtering functions are made compatible with the sensitivity of the broadband receiver so as to retain only the detected frequencies in the model. The theoretical model showed good agreement with experimental results.

Effect of metallization on the power flow angle of SH0 waves in thin piezoelectric plates

The anisotropy of the angle between the phase and group velocity (power flow angle, PFA) as well as the influence of electrical boundary conditions on this angle have been studied for shear-horizontal fundamental (SH0) acoustic waves in thin piezoelectric plates of lithium niobate (LNO) and potassium niobate (KNO). Both LNO and KNO crystals possess orientations at which the PFA for SH0 waves reaches large values (17° and 48°, respectively). It is established that metallization of the piezoelectric plate surface can significantly change PFA values, in particular, by 18° and 55° for Y-X + 25° cut plates of LNO and KNO, respectively.

New method of change in temperature coefficient delay of acoustic waves in thin piezoelectric plates

As is well-known, the development of high-effective and thermostable acoustic devices assumes using the acoustic waves with high coefficient of electromechanical coupling (K2) and low temperature coefficient of delay (TCD). At present, it also is well-known that fundamental shear horizontal (SH0) acoustic waves in thin piezoelectric plates possess by significantly more electromechanical coupling compared to surface acoustic waves (SAW) in the same material. However, although the value of TCD of SH0 waves is insignificantly less than for SAW, this is not enough for development of thermostable devices. This paper suggests a new way of decreasing TCD of SH0 waves in piezoelectric plates at a high level of electromechanical coupling. This way assumes to use the structure containing the piezoelectric plate and liquid with the special dependence of permittivity on temperature. Theoretical and experimental investigation showed that, for SH0 wave in YX LiNbO3 plate at hf = 700 m/s (h = plate thickness, f = wave frequency) the presence of butyl acetate can decrease the value of TCD by six times at K2 = 30%. In a whole the obtained results open the wide prospect of using SH0 wave in thin piezoelectric plate for development of high effective and thermo-stable acoustic devices.

On the impact of anisotropy on dispersion spectra of acoustic waves in plates

A brief overview is given of specific features that can (or cannot) appear in the dispersion spectra of traction-free elastic homogeneous plates due to anisotropy. Its effect on the overall spectral configuration and on the short and long wave trends is illuminated with a link to anisotropic traits of bulk and surface waves. Relevant classical and recent results are put together, and new points are established. To cite this article: A.L. Shuvalov, C. R. Mecanique 334 (2006).