I. A. Nedospasov

Unusual energy properties of leaky backward Lamb waves in a submerged plate

&NA; It is found that leaky backward Lamb waves, i.e. waves with negative energy‐flux velocity, propagating in a plate submerged in a liquid possess extraordinary energy properties distinguishing them from any other type of waves in isotropic media. Namely, the total time‐averaged energy flux along the waveguide axis is equal to zero for these waves due to opposite directions of the longitudinal energy fluxes in the adjacent media. This property gives rise to the fundamental question of how to define and calculate correctly the energy velocity in such an unusual case. The procedure of calculation based on incomplete integration of the energy flux density over the plate thickness alone is applied. The derivative of the angular frequency with respect to the wave vector, usually referred to as the group velocity, happens to be close to the energy velocity defined by this mean in that part of the frequency range where the backward mode exists in the free plate. The existence region of the backward mode is formally increased for the submerged plate in comparison to the free plate as a result of the liquid‐induced hybridization of propagating and nonpropagating (evanescent) Lamb modes. It is shown that the Rayleighs principle (i.e. equipartition of total time‐averaged kinetic and potential energies for time‐harmonic acoustic fields) is violated due to the leakage of Lamb waves, in spite of considering nondissipative media. HighlightsAbnormal energy properties of leaky backward Lamb waves.Zero total energy flux.Violation of the Rayleighs principle of equipartition of kinetic and potential energies.Inequality of group and energy velocities.

Pure shear backward waves in the X-cut and Y-cut piezoelectric plates of potassium niobate

The problem of the existence of pure shear backward waves and waves with zero group velocity is investigated for X-cut and Y-cut plates of orthorhombic crystal of potassium niobate, which distinguishes from the other crystals by exceptionally strong piezoelectric effect. The secular equations of the problem are derived in an explicit analytical form and they are studied numerically in the case of crystal-vacuum interface. Two factors contributing to the appearance of backward waves are identified: the negative displacement of the rays of bulk shear waves at oblique reflection from the surface in piezoelectric crystals and the concavity in cross section of the slowness surface for bulk shear waves near the X axis of the potassium niobate plate. The wide frequency ranges of the existence of symmetric and antisymmetric backward waves of the first and second orders are numerically found in the X-cut plate, for which both of these factors affect. To study the dispersion spreading of backward shear wave pulses, it is suggested to apply the parabolic equation corresponding to the second approximation in the dispersion theory. It is demonstrated that the “diffusion” coefficient in this equation vanishes at certain frequencies, leading to significant suppression of the dispersion distortions in the pulses of the waves under study.

Forward and Backward Acoustic Waves in Crystals with High Piezoactivity and Dielectric Permittivity

Results are presented from studying the characteristics of acoustic waves of different types in plates of ceramic materials with high piezoactivity and dielectric permittivity (e.g., 0.95(Na0.5Bi0.5)TiO3–0.05BaTiO3, (K,Na)(Nb,Ta)O3, and Ba(Zr0.2Ti0.8)O3–50(Ba0.7Ca0.3)TiO3). The dependences of the phase velocities and electromechanical coupling coefficients of these waves on parameter hf (where h is the thickness of a plate, and f is the frequency of a wave) are calculated for directions XY and YX of propagation. It is found that the investigated materials are characterized by frequency ranges of the existence of backward acoustic waves whose phase and group velocities are oriented in different directions. The existence of extremely broad frequency ranges that depend very weakly on a change in the electrical boundary conditions on the surface of a plate is established for waves with negative group velocity in the case of a 0.95(Na0.5Bi0.5)TiO3–0.05BaTiO3 single crystal. It is shown that the electromechanical coupling coefficient of acoustic waves in the investigated materials is greatest for an SH1-wave in YX Ba(Zr0.2Ti0.8)O3–50(Ba0.7Ca0.3)TiO3, and can be as high as 7‒30% in the range hf = 1330–2000 m/s.

Leaky backward Lamb waves in various isotropic and anisotropic plate/liquid systems

The basic characteristics of leaky backward Lamb waves are investigated theoretically and numerically in various combinations of isotropic (aluminum, steel) and anisotropic (YX-NBBT95/5, YX-LiNbO3) plates and surrounding liquids (water, petrol, liquid helium). The phase velocity and attenuation, the group and energy flux velocities, the energies and energy fluxes are among the studied characteristics. It is proved in general anisotropic piezoelectric case that (i) the total (integrated over the depth of the plate and in the liquid) time-averaged energy flux for the leaky backward Lamb waves is identically equal to zero, (ii) the total (integrated over the depth of the plate and in the liquid) time-averaged kinetic and potential energies are not equal to each other, (iii) the energy flux velocity is not equal to the quantity commonly referred to as the group velocity. It follows from our analysis that anisotropy of plates gives a new opportunity to reduce the losses caused by the leakage up to zero at the points of thickness resonances and the backward modes appearing, contrary to isotropic plates where such losses are unavoidable.

Features of propagation and conversion of acoustic waves in plates with nonuniform thickness

The numerical simulation of propagation of the S1 Lamb mode as a pulse through a waveguide with defect is performed with the use of the finite-element method. As a defective waveguide, an isotropic aluminum plate with a groove placed asymmetrically relative to the center is considered. The groove depth is half the plate thickness. It is shown numerically that propagation of the S1 wave in the groove is ensured owing to conversion of this wave at the groove edges into the lower-order mode and the inverse conversion.

Backward acoustic plate waves: Features of properties and possible applications in microelectronic devices

An overview is given of the results of recent and new studies by the authors of this work on topics related to backward acoustic waves of pure-shear type and Lamb type in piezoelectric, crystal, and isotropic plates with free and liquid-loaded surfaces. Various physical mechanisms giving rise to such waves are revealed and quantitatively described by the use of asymptotic expansion of the secular equations and the perturbation theory. The peculiarities of properties of leaky backward waves are considered. The possible applications of backward waves in microelectronic devices (such as sensors et al.) are discussed.

Mechanisms of appearance of backward shear-horizontal waves in potassium niobate plates

The backward waves with opposite directions of energy transport and phase velocity are in the focus of current studies in physics. Besides they are of interest for possible technical applications. This type of wave motion was previously studied in acoustics mainly in the case of Lamb modes. Nevertheless, shear-horizontal (SH) plate modes, as known, can also be backward waves if the plates are piezoelectric. However, SH backward waves were never observed experimentally. The reason for that is a very narrow frequency range where these waves are found numerically in common piezoelectric materials like ZnO with a relative frequency range of only 2•10−5. As we have recently shown [J. Commun. Technol. Electron., November, 2016], the situation is opposite in the case of superstrong piezoelectric crystals of potassium niobate, for which the wide frequency ranges of the existence of backward waves occur in the X-cut plates, while they are absent in the Y-cut plates. The aim of the present work is to study quantitatively the possible mechanisms that affect the appearance of waves under consideration.

Influence of conductive and viscous liquid on the properties of the Bleustein-Gulyaev wave in potassium niobate crystal

Anomalous resisto-acoustic effect is a fundamental property for weakly inhomogeneous acoustic waves. Due to this effect the velocity of such waves initially increases, achieves the maximum and only then decreases with increasing conductance of a layer or media placed at the surface of piezoelectric half-space. Earlier it has been shown that this effect exists for aforementioned waves propagating in contact with conductive liquid. In this paper we investigate the influence of conductive liquid viscosity on this effect.

Influence of liquid on properties of backward acoustic waves in piezoelectric plates

In the paper the characteristics of shear-horizontal direct and backward acoustic waves of the higher orders propagating in XY potassium niobate plates in band including the cutoff frequencies have been theoretically investigated. It also has been theoretically investigated the influence of nonviscous and nonconductive liquid on their properties. It has been found that the presence of liquid are reduced the velocity of waves under study. The range of the backward wave existence is increased with increasing of the wave order number.

Analytical theory of thickness acoustic resonances in liquid drop on solid substrate

The analytical theory of thickness acoustic resonances in a liquid droplet lying on a solid substrate is developed in linear approximation using the following three approaches. The droplet is considered as analog of (i) laser resonator, (ii) plano-convex piezoelectric resonator, (iii) hemi-spheroidal cavity. All three methods in use give the same resonance frequencies and the same eigenmodes for thin drops. The effect of nonlinearity is studied using the perturbation theory based on the complex reciprocity relation (Auld, 1973). The account of nonlinearity shows that the drop on the substrate can behave like a self-controlled acoustic analog of laser resonator in which the vibrations are able to move the upper reflective mirror and to change its shape.