Thickness-twist Waves Research Articles

Effects of the external magnetic field on propagation of thickness-twist waves in inhomogeneous plates

Effects of the external magnetic field on propagation of thickness-twist waves in inhomogeneous plates

Research on tunable characteristics of trapped thickness-twist waves in a magneto-elastic inhomogeneous plate

Research on tunable characteristics of trapped thickness-twist waves in a magneto-elastic inhomogeneous plate

Thickness-twist waves in the nanoplates with flexoelectricity

The effects of flexoelectricity on thickness-twist waves propagating in the nanoplates are analytically investigated. Detailed calculations are performed for nonpiezoelectric material using the method of reverberation-ray matrix (MRRM), by which the numerical instability usually encountered in the conventional methods can be successfully avoided. Based on the derived characteristic equation, the dispersion relations, phase velocity and group velocity of the structures with different geometry and material parameters are subsequently plotted and compared. The numerical results show that the flexoelectric effect is really essential and cannot be neglected to predict wave propagation behavior especially in the nanoscale structures.

Shear-horizontal piezoelectric waves in an aluminum nitride film on a silicon substrate

ABSTRACTThe propagation of shear-horizontal waves in a piezoelectric film of aluminum nitride on a silicon substrate is studied. Three different electrode configurations are considered for thin film acoustic wave resonator application. A theoretical analysis is performed. The equations of linear piezoelectricity and anisotropic elasticity are used for the film and the substrate, respectively. Real and imaginary dispersion curves as well as electromechanical mode shapes are obtained. The effects of electrode configuration on the distribution of the electromechanical fields and the dispersion curves of long thickness-twist waves as well as energy trapping are examined.

Propagation of shear-horizontal waves in piezoelectric plates of cubic crystals

Shear-horizontal waves in a piezoelectric plate of cubic crystals are studied theoretically. Both electroded and unelectroded plates are considered. Exact solutions from the equations of linear piezoelectricity are obtained. The dispersion curves and the distributions of the mechanical displacement and electric potential are presented. There exists a nondispersive face-shear wave. The rest of the waves are dispersive thickness-twist waves. The waves separate into symmetric and antisymmetric groups about the plate middle plane. The dispersion curves for electroded and unelectroded plates are very similar to each other for real wave numbers but have qualitatively different behaviors for pure imaginary wave numbers. For unelectroded plates, neglecting the electric field in the surround free space does not have significant effects.

Propagation of thickness-twist waves in elastic plates with periodically varying thickness and phononic crystals

We study the propagation of thickness-twist (TT) waves in a crystal plate of AT-cut quartz with periodically varying, piecewise constant thickness. The scalar differential equation by Tiersten and Smythe is employed. The problem is found to be mathematically equivalent to the motion of an electron in a periodic potential field governed by Schrodinger’s equation. An analytical solution is obtained. Numerical results show that the eigenvalue (frequency) spectrum of the waves has a band structure with allowed and forbidden bands. Therefore, for TT waves, plates with periodically varying thickness can be considered as phononic crystals. The effects of various parameters on the frequency spectrum are examined.

Investigation of trapped thickness-twist waves induced by functionally graded piezoelectric material in an inhomogeneous plate

The effect of functional graded piezoelectric materials on the propagation of thickness-twist waves is investigated through equations of the linear theory of piezoelectricity. The elastic and piezoelectric coefficients, dielectric permittivity, and mass density are assumed to change in a linear form but with different graded parameters along the wave propagation direction. We employ the power-series technique to solve the governing differential equations with variable coefficients attributed to the different graded parameters and prove the correction and convergence of this method. As a special case, the functional graded middle layer resulting from piezoelectric damage and material bonding is investigated. Piezoelectric damaged material can facilitate energy trapping, which is impossible in perfect materials. The increase in the damaged length and the reduction in the piezoelectric coefficient decrease the resonance frequency but increase the number of modes. Higher modes of thickness-twist waves appear periodically along the damaged length. Moreover, the displacement of the center of the damaged portion is neither symmetric nor anti-symmetric, unlike the non-graded plate. The conclusions are theoretically and practically significant for wave devices.

Overtone frequency spectra for ξ3-dependent modes in AT-cut quartz resonators [Correspondence

We study straight-crested waves and vibration modes with spatial variations along the x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> direction only in an AT-cut quartz plate resonator. The equations of anisotropic elasticity are used. Dispersion relations for face-shear and thickness-twist waves in unbounded plates are plotted. Frequency spectra are obtained for face-shear and thickness-twist vibrations of finite plates in which these modes are coupled by boundary conditions. Most importantly, our analysis produces the frequency spectra for overtone modes which do not seem to have been obtained before for x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> -dependent modes. Numerical results for third- and fifth-overtone AT-cut quartz resonators are presented, showing that higher-order overtone modes are associated with more mode couplings.

Analysis of shear-horizontal waves propagating in a piezoelectric plate in contact with a semi-infinite fluid for liquid sensor application

We study the propagation of shear-horizontal waves in a piezoelectric plate of monoclinic crystals in contact with a semi-infinite viscous fluid as an acoustic wave sensor for measuring fluid viscosity or density. Mindlin's first-order theory for piezoelectric plates and the theory of Newtonian fluids are used. Approximate dispersion relations for long face-shear and thickness-twist waves are given analytically. Numerical results showing the effects of the fluid and the piezoelectric coupling in the plate on basic wave propagation characteristics are presented.

Thickness-twist and face-shear waves in piezoelectric plates of monoclinic crystals

We study the propagation of thickness-twist and face-shear waves in piezoelectric plates of monoclinic crystals, which include rotated Y-cut quartz and langasite as special cases. The equations of linear piezoelectricity are used. Exact solutions are obtained for both fully-electroded and unelectroded plates. Dispersion relations are plotted for both AT-cut quartz and Y-cut langasite plates. The difference in frequencies between the exact piezoelectric solutions obtained in the present paper and the approximate elastic solutions in the literature is found to be of the order of 1%, which is significant in acoustic wave resonator and sensor applications.

Energy trapping of thickness-twist waves in an inhomogeneous piezoelectric plate with an imperfect joint

Energy trapping of thickness-twist waves in an inhomogeneous piezoelectric plate with an imperfect joint

Propagation of thickness-twist waves in an inhomogeneous piezoelectric plate with an imperfectly bonded interface

The propagation of thickness-twist waves in an inhomogeneous piezoelectric plate with an imperfectly bonded interface is investigated. Based on the spring-type relation, the imperfectly bonded interface is dealt with, and the exact solution is obtained from the equations of the linear theory of piezoelectricity. The amplitude ratio between the incident wave and the reflected wave, the displacement component and the stress component are all obtained and plotted. Both theoretical analysis and numerical examples show that the effect of the mechanical imperfection on the wave propagation is more evident than that of the electrical imperfection. When the incident wave frequency and the mechanical imperfect parameter meet some particular relation, no reflected waves can appear in the piezoelectric plate. The results are of fundamental importance to the design of resonators and other devices when imperfect joints are considered.

Propagation of thickness-twist waves in a piezoelectric ceramic plate in contact with viscous fluids

We study theoretically the propagation of thickness-twist waves in an unbounded piezoelectric ceramic plate with unattached electrodes and viscous fluids between the plate surfaces and the electrodes. Based on the theories of piezoelectricity and viscous fluids, an equation that determines the dispersion relations of the waves is obtained, showing the dependence of the phase velocity on material and geometric parameters. Due to the viscosity of the fluid, the dispersion relations are complex in general, representing damped waves with attenuation. The dispersion relations obtained can reduce to the results of a few special cases with known results. The results of the present paper are useful for developing and designing fluid sensors for measuring fluid viscosity or density.

Propagation of thickness-twist waves in a piezoelectric ceramic plate with unattached electrodes

We analyze the propagation of thickness-twist waves in an unbounded piezoelectric ceramic plate with air gaps between the plate surfaces and two electrodes. These waves are also called anti-plane or shear-horizontal waves with one displacement component only. An exact solution is obtained from the equations of the linear theory of piezoelectricity. Dispersion relations of the waves are obtained and plotted. Results show that the wave frequency or speed is sensitive to the air gap thickness. This effect can be used to manipulate the behavior of the waves and has implications in acoustic wave devices.

Effect of mass layer stiffness on propagation of thickness-twist waves in rotated Y-cut quartz crystal plates

We analyze the effect of mass layer stiffness on thickness-twist waves propagating in a rotated Y-cut quartz crystal plate with thin mass layers on its surfaces. An equation that determines the dispersion relation of the waves is given and is solved numerically. Quantitative results of the effect of the mass layer stiffness on wave frequencies are presented. These results are important to the understanding and design of resonators and mass sensors.

Propagation of thickness-twist waves through a joint between two semi-infinite piezoelectric plates

We study the propagation of thickness-twist waves through a joint between two semi-infinite piezoelectric plates of crystals with 6-mm symmetry or polarized ceramics. An exact solution from the three-dimensional equations of piezoelectricity is obtained. The solution shows the cutoff of certain waves and the presence of localized electromechanical fields near the joint. The results are of fundamental importance to the understanding and design of resonators and other devices made from plates of these materials, in particular thin film resonators of ZnO and AlN.

Propagation of thickness-twist waves in a multi-sectioned piezoelectric plate of 6 mm crystals

We study thickness-twist vibrations and waves in an unbounded, multi-sectioned piezoelectric plate of crystals with 6 mm symmetry or polarized ceramics. An exact solution from the three-dimensional equations of piezoelectricity is obtained. Basic vibration and wave propagation characteristics are calculated based on the solution. The results are useful in the understanding and design of plate resonators, filters and acoustic wave sensors of ZnO, AlN and polarized ceramics.

Effects of Piezoelectric Coupling on Bechmann's number for thickness-twish waves in a plate of hexagonal crystals

Solutions for thickness-twist waves in a piezoelectric plate of 6-mm crystals with surface mass layers are obtained. The solutions are used to determine Bechmann's number for designing electrode size of devices operating with these waves. This generalizes the existing knowledge on Bechmann's number by the inclusion of piezoelectric coupling. It is shown that this coupling plays a role as important as or more important than the electrode inertia. The results are of fundamental importance to resonator design, in particular thin film resonators of ZnO and AlN.

Propagation of thickness-twist waves in a quartz plate with asymmetric mass layers

An exact solution is obtained for thickness-twist waves in a quartz plate with asymmetric mass layers. A simple, approximate expression for cutoff frequencies is given.

Rotation sensitivity of waves propagating in a rotating piezoelectric plate

The rotation effect on the characteristics of waves propagating in a piezoelectric plate is studied in the framework of linear piezoelectricity including Coriolis and centrifugal forces. The rotation sensitivity of the wave dispersion relations is analyzed in details for polarized ceramic plates and for the lowest thickness-shear and the lowest thickness-twist waves because of the particular importance of these modes for gyroscope applications. The analysis shows that the frequency shifts monotonically with the increasing rotation rate and the rotation sensitivity of long waves is substantially greater than that of short waves. Generally, plates with shorted electrode surfaces have higher rotation sensitivity than plates with free-charge surfaces. For long waves and for small rotation rate relative to the wave frequency, the frequency shifts with rotation rate, linearly for plates with shorted electrode surfaces and nonlinearly with a nearly flat initial tangent for plates with free-charge surfaces. These rotation sensitivity characteristics are of interest for the development of rotation sensors and other piezoelectric devices for which frequency insensitivity to rotation is desired.