Face-shear Mode Research Articles

Electromechanical modelling of l-shaped bending-torsion piezoelectric energy harvesting systems

Piezoelectric energy harvesting (PEH) has become an important concept in recent years, aiming to harvest energy from various mechanical vibrations. However, a significant gap has been noticed in the multimodal and multidirectional analytics of PEHs. In this context, this paper proposes an innovative approach to introduce a novel multimodal and multidirectional PEH design, which exploits both the face extension mode (d31) and the face shear mode (d36), to target low-frequency environments. The study investigates three bending-torsion l-shaped bimorph PEHs, namely H1, H2, and H3. To evaluate the performance of the proposed PEHs, a distributed parameter model is developed based on the assumptions of the Euler-Bernoulli beam. The validity of the model is confirmed by analytical, numerical, and experimental results from previous work. The exploitation of the d36 mode enhances the power output of H1, H2, and H3 by 67.95 %, 43.66 %, and 31.83 respectively. The three PEHs performances are compared quantitatively and qualitatively, and H1 is found to be the most efficient among them. The PEH H1 requires a single excitation to perform the coupled bending-torsion motions, resulting in an outstanding average power output of 54.66 µW, which outperforms the other two PEHs by tenfold. The use of the d36 modes to expand the frequency bandwidth and improve the power output presents an excellent innovative and practical value for piezoelectric energy harvesting.

Exploring of piezoelectric crystal GdBa3(PO4)3 featuring pure face-shear mode and strong piezoelectric response for SH0 wave transducer application

The fundamental shear horizontal (SH0) wave is highly desired for structural health monitoring (SHM) applications because of its advantageous non-dispersive, and minimal energy loss properties. However, the generation and detection of a pure SH0 wave solely using traditional piezoelectric materials possess a considerable challenge owing to their complex piezoelectric response. To effectively address this issue, a new piezoelectric crystal GdBa3(PO4)3 (GdBP) featuring a pure face-shear vibration mode was successfully grown using the Czochralski method. Notably, The GdBP crystal showcases a stronger shear piezoelectric strain coefficient (d14=15.2 pC/N), surpassing some of the extensively studied crystals. A GdBP-based SH0 wave transducer was first designed guided by the numerical simulation. The experiment results show the functions of exciting and detecting stable SH0 wave signals along four main directions (i.e. 0°, 90°, 180°, and 270°) with the operation temperature exceeding 500 °C, and further manifest the reliable capability in defect detection. Our results highlight the great potential of GdBP-based SH0 wave piezoelectric transducer and lead to an effective SHM applications, particularly in harsh environments.

Monolithic piezoceramic actuators with a twist

Designing artificial structures with heterogeneous elements and manipulating their interface coupling ways usually bring in synthetic neo-nature to functional devices. For piezoceramic devices, the deformation response refers to a variety of extensional, contractional, or shear modes of crystals, and also relies on boundary conditions from morphology design. However, to pursue fundamental torsion actuation in an integrated piezoceramic component is still a long-term tough task due to nil twist mode limited by microscopic crystal mirror symmetry. Herein, we demonstrate a design of cofired monolithic actuators to originally overcome this obstacle. The prototype device is composed of two sets of stacked actuation subunits that work on artificially reverse face shear modes, and their chiral stiffness couplings will synergistically contribute to synthetic twist outputs at a broad bandwidth. Finite element simulation reveals twist displacements are highly tunable by manipulating the geometrical dimensions. Transverse deflection measurements manifest the stable and sizeable linear actuation response to applied electric fields (around 3.7 µm under 40 V at 1 Hz). Importantly, the design actually introduces a more general route to enable arbitrary modes and actuation states in integrated piezoceramic components.

Electro-elastic features of YBa3(PO4)3 and YbBa3(PO4)3 crystals with pure face-shear mode for acoustic wave sensor applications

The fundamental shear horizontal (SH0) waves have been proved to be a very useful method for non-destructive testing due to their non-dispersive characteristics. Currently, although several methods have been proposed to generate SH0 waves, it is still a challenge to obtain pure SH0 wave mode efficiently. Herein, in this study, non-centrosymmetric YBa3(PO4)3 (YBP) and YbBa3(PO4)3 (YbBP) crystals with pure face-shear mode were grown via the traditional Czochralski pulling method at temperatures above 1800 °C. High resolution X-ray diffraction was carried out to evaluate the crystalline quality. Results showed that the YBP and YbBP crystals were of good quality, with the full width at half-maxima being on the order of 42.5″ and 52.3″, respectively. Moreover, the full set of electro-elastic constants for the YBP and YbBP crystals were determined and collated using a combination of impedance and pulse-echo methods. The piezoelectric coefficient (d14) of the YBP and YbBP crystals were determined to be 10.6 pC/N and 11.4 pC/N, respectively, corresponding to the electromechanical coupling coefficient (k14) equal to 15.4% and 15.9%, exhibiting large and pure face-shear vibration mode. Collectively, these results indicate that the YBP and YbBP crystals are promising for acoustic wave sensing application.

High sensitivity face shear magneto-electric composite array for weak magnetic field sensing

A magnetic field sensor is designed and fabricated using a piezoelectric face shear mode Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMN–PT)/Metglas magneto-electric (ME) composite. An outstanding ME coupling coefficient up to 1600 V/(cm Oe) was experimentally achieved, being ∼50% higher than the value from the extensional PMN–PT/Metglas ME composite with the same volume. The detection limit was found to be 2 × 10−6 Oe for the DC magnetic field, while it was 2 × 10−8 Oe for the AC magnetic field. The sensitivity of the face shear mode PMN–PT/Metglas ME composite is about one order of magnitude higher than that of a 32 extensional mode PMN–PT/Metglas based ME composite in sensing a weak DC magnetic field. A sensing array was also designed based on the ME composite to image weak DC magnetic fields, demonstrating a great potential promising for sensing weak magnetic fields.

Long-distance structural health monitoring of buried pipes using pitch-catch T(0,1) wave piezoelectric ring array transducers

In modern industries, long-distance guided wave inspection has been routinely used for various types of pipelines. The usage of T(0,1) wave is always of great interests since it is the only non-dispersive wave mode in pipes. In this work, a pair of pitch-catch piezoelectric ring arrays were proposed for long-distance structural health monitoring (SHM) of buried pipes. Firstly, the working principle of the proposed transducer was introduced. Next, the performances of thickness-shear (d15) and face-shear (d24) modes based piezoelectric ring transducers in T(0,1) wave generation and reception were comparatively tested. It was found that at most frequencies, it is best to employ the d15 ring as the exciter and the d24 ring as the receiver. Then, the signal-to-noise ratio (SNR) of the generated T(0,1) wave and its attenuation in pipes with different coating conditions were investigated to estimate the detectable distance using the proposed transducer. Results showed that after applying acoustical isolation layer on pipes, the proposed ring transducers can inspect buried pipes over 20 m. Finally, the performance of the ring transducers in defect detection was validated. This work is expected to provide a promising solution to long-distance SHM of buried pipes.

Quantitative domain engineering for realizing d36 piezoelectric coefficient in tetragonal ceramics

Piezoelectric devices based on d36 mode are remarkably stable that depolarization rarely occurs in d36 face shear mode, because d36 mode is completely different from d15 thickness shear mode, where the applied electric field is perpendicular to poling direction and depolarization is ineluctable due to 90° dipole rotation. However, piezoelectric ceramics conventionally possess three piezoelectric coefficients (i.e., d33, d31, and d15), while d36 only exists in single crystals of specific point groups and cut directions. In this work, we propose a method to realize d36 piezoelectric coefficient in tetragonal piezoelectric ceramics by mechanical and electric domain engineering. This method is successfully applied in bismuth scandium-lead titanate (abbreviated as BS-PT) high-temperature piezoelectric ceramics with a resultant d36 up to 160 pC/N, which broadens the application of BS-PT ceramics, such as face shear actuator, energy harvester, transducer, etc. We find that domain engineering by transversal electric poling is preferred compared with the transversal mechanical poling, due to the simpler process, higher reliability, and higher resultant d36 piezoelectric coefficient. By combining the Diffraction-Plane-Transformation (DPT) model with the domain engineering via transversal electric poling, we demonstrate a quantitative domain engineering method for the first time, which could be used for optimizing the piezoelectric properties by precise design of the domain structures in piezoelectric materials.

A Face-Shear Mode Piezoelectric Array Sensor for Elasticity and Force Measurement.

We present the development of a 6 × 6 piezoelectric array sensor for measuring elasticity and force. The proposed sensor employs an impedance measurement technique, sensing the acoustic load impedance of a target by measuring the electrical impedance shift of face-shear mode PMN–PT (lead magnesium niobate–lead titanate) single crystal elements. Among various modes of PMN–PT single crystals, the face-shear mode was selected due to its especially high sensitivity to acoustic loads. To verify the elasticity sensing performance, gelatin samples with different elastic moduli were prepared and tested. For the force measurement test, different magnitudes of force were loaded to the sensing layer whose acoustic impedance was varied with applied forces. From the experimental results, the fabricated sensor showed an elastic stiffness sensitivity of 23.52 Ohm/MPa with a resolution of 4.25 kPa and contact force sensitivity of 19.27 Ohm/N with a resolution of 5.19 mN. In addition, the mapping experiment of elasticity and force using the sensor array was successfully demonstrated.

SH guided wave excitation by an apparent face-shear mode (d36) piezocomposite transducer: experiments and theory

The fundamental shear horizontal (SH0) wave in plate-like structures is of practical importance in structural health monitoring (SHM) due to its non-dispersive characteristics. However, compared with Lamb waves, SH0 wave is less used in practice since it is difficult to be excited by using conventional piezoelectric transducers. In this work, an apparent face-shear mode (d36) piezocomposite transducer was proposed to excite and receive SH0 wave. The piezocomposite transducer was made up of epoxies and several hollow PZT squares of different sizes. The face-shear d36 mode was synthetized by the thickness-shear deformation of each side of the hollow PZT squares. Both finite element simulations and experimental testings showed that the apparent d36 piezocomposite transducer was capable of exciting pure SH0 wave along four main directions (0°, 90°, 180° and 270°) from 70 to 150 kHz. Moreover, the piezocomposite transducer can filter Lamb waves and receive SH0 wave only over a wide frequency range from 70 to 370 kHz. Based on Huygens’ principle and the method of solving inclusion problem, an eigenstrain-based theoretical model was then proposed to describe the SH0 wave field generated by face-shear transducers. Explicit analytical expressions for the piezocomposite transducer were successfully obtained and their accuracies were verified by both experiments and finite element simulations. Furthermore, some general guidelines based on the analytical model were presented for optimization of the transducer’s dimensions. The proposed apparent d36 piezocomposite transducer may be a good candidate for exciting and receiving low frequency SH0 wave in SHM systems, since it is lightweight and shows better surface conformability than PZT wafers.

Bismuth-Based Oxyborate Piezoelectric Crystals: Growth and Electro-Elastic Properties

The non-centrosymmetric bismuth-based oxyborate crystals have been extensively studied for non-linear optical, opto-electric and piezoelectric applications. In this work, single crystal growth and electro-elastic properties of α-BiB3O6 (α-BIBO) and Bi2ZnB2O7 (BZBO) crystals are reported. Centimeter-sized α-BIBO and BZBO crystals were grown by using the Kyropoulos method. High resolution X-ray diffraction tests were performed to assess the crystal quality. The full-width at half-maximum values (FWHM) of the rocking curves were evaluated to be 35.35 arcsec and 47.85 arcsec for α-BIBO and BZBO samples, respectively. Moreover, the electro-elastic properties of α-BIBO and BZBO crystals are discussed and summarized, based on which the radial extensional and the face shear vibration modes were studied for potential acoustic device applications. The radial extensional mode electro-mechanical coupling factors kp were evaluated and found to be 32.0% and 5.5% for α-BIBO and BZBO crystals, respectively. The optimal crystal cuts with face shear mode were designed and found to be (YZt)/−53° (or (YZt)/37° cut) for α-BIBO crystal, and (ZXt)/±45° cut for BZBO crystal, with the largest effective piezoelectric coefficients being in the order of 14.8 pC/N and 8.9 pC/N, respectively.

A Comparative Study of Three Types Shear Mode Piezoelectric Wafers in Shear Horizontal Wave Generation and Reception.

Guided wave-based inspection has emerged as a promising tool to evaluate the reliability of key components in modern industries. The fundamental shear horizontal (SH0) wave is always of great interests for plate-like structures because of its non-dispersion characteristics. However, the generation and reception of SH0 wave using piezoelectric wafers is not straightforward. In this paper, we firstly define three types shear mode piezoelectric wafers, i.e., the conventional in-plane poled thickness-shear (d15) mode, the thickness-poled thickness-shear (d15) mode, and the face-shear (d24) mode. Then, finite element simulations were conducted to demonstrate their performance in SH wave generation and reception. The results indicated that the face shear d24 wafer can generate almost single mode SH0 wave, while both types of d15 wafers would generate Lamb waves and SH0 wave simultaneously. Finally, experiments were carried out to check the efficiency of different shear mode piezoelectric wafers in SH0 wave generation and reception. The results indicated that the d24 wafer can generate and receive SH0 wave of high signal to noise ratio (SNR) with high energy conversion efficiency, while the in-plane poled d15 wafer would generate SH0 wave of high amplitude and acceptable SNR but with relatively low energy conversion efficiency. The performances of thickness-poled d15 wafer was not as good as the other two in both SH wave generation and reception. This work will be helpful for the applications of SH waves in plate-like structures.

Generation and reception of shear horizontal waves using the synthetic face-shear mode of a thickness-poled piezoelectric wafer

The guided wave based inspection technique has been playing an important role in modern industries due to its capability in rapid detection of large structures. Among all the wave modes in plate-like structures, the fundamental shear horizontal wave (SH0) is of great importance since it is the unique non-dispersive mode. However, the generation and reception of SH0 wave using piezoelectrics is always a challenge. In this work, we synthesized face-shear deformation mode in a thickness-poled piezoelectric wafer and successfully excited/received SH0 wave in a thin aluminum plate. Firstly, the frequency response of the proposed wafer was analyzed using the finite element method (FEM) to show that the face-shear deformation can be synthesized via applying anti-parallel electric fields on different parts of the wafer. Subsequently, time-transient FEM simulations were carried out to predict its capacity in generation/reception of SH0 wave. Finally, experiments were conducted to examine the performance of the proposed wafer on SH0 wave generation/reception. The obtained results indicate that the synthetic face-shear piezoelectric wafer can generate SH0 wave along two principal directions (0° and 90°) with the amplitudes symmetric along the 45° direction. The amplitude of the generated SH0 wave reached its maxima along the principal direction and decreased to nearly zero at 45° direction, which is in good agreement with the FEM results. Besides, the wafer can only receive SH0 wave in a wide range of frequency, i.e., it can act as an inherent wave filter. Due to its compact size and easy fabrication, the proposed wafer has a great potential in promoting the applications of SH0 wave in nondestructive testing and structural health monitoring.

Excitation and reception of pure shear horizontal waves by using face-shear d24 mode piezoelectric wafers

The fundamental shear horizontal (SH0) wave in plate-like structures is of great importance in non-destructive testing (NDT) and structural health monitoring (SHM) as it is non-dispersive, while excitation or reception of SH0 waves using piezoelectrics is always a challenge. In this work, we firstly demonstrate via finite element simulations that face-shear piezoelectrics is superior to thickness-shear piezoelectrics in driving SH waves. Next, by using a newly defined face-shear d24 PZT wafer as an actuator and face-shear d36 PMN-PT wafers as sensors, pure SH0 wave was successfully excited in an aluminum plate from 130 to 180 kHz. Then, it was shown that the face-shear d24 PZT wafer could receive the SH0 wave only and filter the Lamb waves over a wide frequency range (120–230 kHz). The directionality of the excited SH0 wave was also investigated using face-shear d24 PZT wafers as both actuators and sensors. Results show that pure SH0 wave can be excited symmetrically along two orthogonal directions (0° and 90°) and the amplitude of the excited SH0 wave can keep over 90% of the maximum amplitude when the deviate angle is within 30°. This work could greatly promote the applications of SH0 wave in NDT and SHM.

Development of an apparent face-shear mode (d36) piezoelectric transducer for excitation and reception of shear horizontal waves via two-dimensional antiparallel poling

The non-dispersive fundamental shear horizontal (SH0) wave is extremely useful in guided-wave-based inspection techniques. However, the generation or reception of the SH0 wave by using a piezoelectric transducer is always a challenge. In this work, first, we realized the apparent face-shear (d36) mode in PbZr1-xTixO3 (PZT) ceramics via two-dimensional antiparallel poling. Then, we demonstrated via finite element simulations that the apparent d36 mode PZT wafer can behave as both a SH0 wave actuator and a SH0 wave sensor. Next, by using the apparent d36 PZT wafer as an actuator and a face-shear d36 0.72[Pb(Mg1/3Nb2/3)O3]-0.28[PbTiO3] crystal as the sensor, almost a pure SH0 wave with a high signal-to-noise ratio was successfully excited in an aluminum plate from 180 kHz to 200 kHz. Later, experiments showed that the proposed apparent d36 PZT wafer can also serve as a sensor to detect the SH0 wave over a wide frequency range (160 kHz to 230 kHz). Finally, the amplitude directivity of the SH0 wave generated by the apparent d36 PZT wafer was also investigated. The wave amplitude reaches its maxima at the main direction (0° and 90°) and then decreases monotonically when the propagation direction deviates from the main directions, with the symmetric axis along the 45° direction. The proposed apparent d36 PZT wafer is very suitable for severing as SH0 wave actuators and sensors in structural health monitoring systems.

Low-temperature phase transition in γ-glycine single crystal. Pyroelectric, piezoelectric, dielectric and elastic properties

Temperature changes in the pyroelectric, piezoelectric, elastic and dielectric properties of γ-glycine crystals were studied in the range 100 ÷ 385 K. The pyroelectric coefficient increases monotonically in this temperature range and its value at RT was compared with that of other crystals having glycine molecules. A big maximum in the d14 component of piezoelectric tensor compared by maximum in attenuation of the resonant face-shear mode were observed at 189 K. The components of the elastic stiffness tensor and other components of the piezoelectric tensor show anomalies at this temperature. The components of electromechanical coupling coefficient determined indicate that γ-glycine is a weak piezoelectric. The real and imaginary part of the dielectric constant measured in the direction perpendicular to the trigonal axis show the relaxation anomalies much before 198 K and the activation energies were calculated. These anomalies were interpreted as a result of changes in the NH3+ vibrations through electron-phonon coupling of the so called “dynamical transition”. The anomalies of dielectric constant ε*11 and piezoelectric tensor component d14 taking place at 335 K are associated with an increase in ac conductivity caused by charge transfer of protons.

Excitation of fundamental shear horizontal wave by using face-shear (d36) piezoelectric ceramics

The fundamental shear horizontal (SH0) wave in plate-like structures is extremely useful for non-destructive testing (NDT) and structural health monitoring (SHM) as it is non-dispersive. However, currently, the SH0 wave is usually excited by electromagnetic acoustic transducers (EMAT) whose energy conversion efficiency is fairly low. The face-shear (d36) mode piezoelectrics is more promising for SH0 wave excitation, but this mode cannot appear in conventional piezoelectric ceramics. Recently, by modifying the symmetry of poled PbZr1−xTixO3 (PZT) ceramics via ferroelastic domain engineering, we realized the face-shear d36 mode in both soft and hard PZT ceramics. In this work, we further improved the face-shear properties of PZT-4 and PZT-5H ceramics via lateral compression under elevated temperature. It was found that when bonded on a 1 mm-thick aluminum plate, the d36 type PZT-4 exhibited better face-shear performance than PZT-5H. We then successfully excite SH0 wave in the aluminum plate using a face-shear PZT-4 square patch and receive the wave using a face-shear 0.72[Pb(Mg1/3Nb2/3)O3]-0.28[PbTiO3] (PMN-PT) patch. The frequency response and directionality of the excited SH0 wave were also investigated. The SH0 wave can be dominated over the Lamb waves (S0 and A0 waves) from 160 kHz to 280 kHz. The wave amplitude reaches its maxima along the two main directions (0° and 90°). The amplitude can keep over 80% of the maxima when the deviate angle is less than 30°, while it vanishes quickly at the 45° direction. The excited SH0 wave using piezoelectric ceramics could be very promising in the fields of NDT and SHM.

Comparative face-shear piezoelectric properties of soft and hard PZT ceramics

The face-shear (d36) mode may be the most practical shear mode in piezoelectrics, while theoretically this mode cannot appear in piezoelectric ceramics because of its transversally isotropic symmetry. Recently, we realized piezoelectric coefficient d36 up to 206pC/N in soft PbZr1-xTixO3 (PZT) ceramics via ferroelastic domain engineering [H. C. Miao and F. X. Li, Appl. Phys. Lett. 107, 122902 (2015)]. In this work, we further realized the face-shear mode in both hard and soft PZT ceramics including PZT-4 (hard), PZT-51(soft), and PZT-5H (soft) and investigated the electric properties systematically. The resonance methods are derived to measure the d36 coefficients using both square patches and narrow bar samples, and the obtained values are consistent with that measured by a modified d33 meter previously. For all samples, the pure d36 mode can only appear near the resonance frequency, and the coupled d36-d31 mode dominates off resonance. It is found that both the piezoelectric coefficient d36 and the electromechanical coupling factor k36 of soft PZT ceramics (PZT-5H and PZT-51) are considerably larger than those of the hard PZT ceramics (PZT-4). The obtained d36 of 160–275pC/N, k36 ∼ 0.24, and the mechanical quality factor Q36 of 60–90 in soft PZT ceramics are comparable with the corresponding properties of the d31 mode sample. Therefore, the d36 mode in modified soft PZT ceramics is more promising for industrial applications such as face-shear resonators and shear horizontal wave generators.

Functional Piezocrystal Characterisation under Varying Conditions.

Piezocrystals, especially the relaxor-based ferroelectric crystals, have been subject to intense investigation and development within the past three decades, motivated by the performance advantages offered by their ultrahigh piezoelectric coefficients and higher electromechanical coupling coefficients than piezoceramics. Structural anisotropy of piezocrystals also provides opportunities for devices to operate in novel vibration modes, such as the d36 face shear mode, with domain engineering and special crystal cuts. These piezocrystal characteristics contribute to their potential usage in a wide range of low- and high-power ultrasound applications. In such applications, conventional piezoelectric materials are presently subject to varying mechanical stress/pressure, temperature and electric field conditions. However, as observed previously, piezocrystal properties are significantly affected by a single such condition or a combination of conditions. Laboratory characterisation of the piezocrystal properties under these conditions is therefore essential to fully understand these materials and to allow electroacoustic transducer design in realistic scenarios. This will help to establish the extent to which these high performance piezocrystals can replace conventional piezoceramics in demanding applications. However, such characterisation requires specific experimental arrangements, examples of which are reported here, along with relevant results. The measurements include high frequency-resolution impedance spectroscopy with the piezocrystal material under mechanical stress 0–60 MPa, temperature 20–200 °C, high electric AC drive and DC bias. A laser Doppler vibrometer and infrared thermal camera are also integrated into the measurement system for vibration mode shape scanning and thermal conditioning with high AC drive. Three generations of piezocrystal have been tested: (I) binary, PMN-PT; (II) ternary, PIN-PMN-PT; and (III) doped ternary, Mn:PIN-PMN-PT. Utilising resonant mode analysis, variations in elastic, dielectric and piezoelectric constants and coupling coefficients have been analysed, and tests with thermal conditioning have been carried out to assess the stability of the piezocrystals under high power conditions.

Realization of face-shear piezoelectric coefficient d36 in PZT ceramics via ferroelastic domain engineering

The piezoelectric face-shear (d36) mode may be the most useful shear mode in piezoelectrics, while currently this mode can only exist in single crystals of specific point groups and cut directions. Theoretically, the d36 coefficient vanishes in piezoelectric ceramics because of its transversally isotropic symmetry. In this work, we modified the symmetry of poled PZT ceramics from transversally isotropic to orthogonal through ferroelastic domain switching by applying a high lateral stress along the “2” direction and holding the stress for several hours. After removing the compression, the piezoelectric coefficient d31 is found much larger than d32. Then, by cutting the compressed sample along the Zxt±45° direction, we realized d36 coefficients up to 206pC/N, which is measured by using a modified d33 meter. The obtained large d36 coefficients in PZT ceramics could be very promising for face-shear mode resonators and shear horizontal wave generation in nondestructive testing.

The properties of thickness-twist (TT) wave modes in a rotated Y-cut quartz plate with a functionally graded material top layer

We propose the use of thickness-twist (TT) wave modes of an AT-cut quartz crystal plate resonator for measurement of material parameters, such as stiffness, density and material gradient, of a functionally graded material (FGM) layer on its surface, whose material property varies exponentially in thickness direction. A theoretical analysis of dispersion relations for TT waves is presented using Mindlin’s plate theory, with displacement mode shapes plotted, and the existence of face-shear (FS) wave modes discussed. Through numerical examples, the effects of material parameters (stiffness, density and material gradient) on dispersion curves, cutoff frequencies and mode shapes are thoroughly examined, which can act as a theoretical reference for measurements of unknown properties of FGM layer.