Full-wave analysis of piezoelectric boundary waves propagating along metallic grating sandwiched between two semi-infinite layers

This paper describes full-wave analysis of piezoelectric boundary acoustic waves (PBAWs) propagating along a metallic grating sandwiched between 2 semi-infinite layers. In the analysis, the finite element method (FEM) is used for the grating region while the spectral domain analysis (SDA) is applied for an isotropic overlay region as well as a piezoelectric substrate region. The combination of the FEM and SDA makes the numerical analysis very fast and precise. As an example, the analysis was made on the PBAWs propagating in an SiO₂ overlay/ Cu grating/rotated Y-cut LiNbO₃ structure. It is shown that both the shear-horizontal (SH) type and Rayleigh-type PBAWs are supported in the structure, and that their velocities are very close to each other. Thus spurious responses due to the Rayleigh-type PBAW should completely be suppressed for device implementation. Discussions are made in detail on the influence of Cu grating thickness, substrate rotation angle, and metallization ratio on excitation and propagation characteristics of the SH- and Rayleigh-type PBAWs.     

Propagation of nonlinear acoustic waves in gallium

We study nonlinear phenomena which occur during strong sound signal propagation in superpure Ga and are due to the perturbation of the electron subsystem in the metal. Although the observations are in qualitative agreement with theoretical concepts in a number of aspects, there are effects which still lack adequate theoretical interpretation, in particular, an oscillatory dependence of the harmonic amplitudes on magnetic field which is linear with respect toH ^1/2, and appreciable nonlinear distortions of the sound pulse envelope accompanied by the acoustic noise generation.     

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.     

Lamb waves in a thin isotropic layer between two anisotropic layers

Attenuative Lamb wave propagation in adhesively bonded anisotropic composite plates is introduced. The isotropic adhesive exhibits viscous behavior to stimulate the poor curing of the middle layer. Viscosity is assumed to vary linearly with frequency, implying that attenuation per wavelength is constant. Attenuation can be implemented in the analysis through modification of elastic properties of isotropic adhesive. The new properties become complex, but cause no further complications in the analysis. The characteristic equation is the same as that used for the elastic plate case, except that both real and imaginary parts of the wave number (i.e., the attenuation) must be computed. Based on the Lowe's solution in finding the complex roots of characteristic equation, the effect of longitudinal and shear attenuation coefficients of the middle adhesive layer on phase velocity dispersion curves and attenuation dispersion curves of Lamb waves propagating in bonded anisotropic composites is visualized numerically.     

Propagation of surface acoustic waves inn-type GaAs films

The effect of nonparabolicity on the amplification of surface acoustic waves in n-type GaAs films is investigated quantum mechanically in the GHz frequency region. Numerical results show that the amplification coefficient for the nonparabolic band structure is enhanced due to the nonlinear nature of the energy band in semiconductors. Moreover, the amplification coefficients in semiconductors depend on the temperature, the electronic screening effect, the frequency of sound waves, the applied electric field, and the thickness of the semiconductor film.Partially supported by National Science Council of the Republic of China.     

Propagation of acoustic waves in unsaturated porous media

A mathematical model of propagation of acoustic waves in a proous medium saturated with a two-phase mixture is proposed. The mechanism of initiation of slow motion as a result of prolonged nondestructive acoustic action is analyzed. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 3, pp. 433–440, May–June, 1998.     

Propagation of detonation waves along a tubular bubble cluster in liquid

The dynamics are studied of axisymmetric two-dimensional detonation waves in liquid with bubbles, where the bubbles are found in the form of a tubular cluster in the axial region of a pipe and where they are arranged in the form of a ring bubble layer. It is demonstrated that such clusters may serve as a waveguide for transmitting pulsed signals which are detonation solitons. It is found that, because of precompression of a bubble cluster by waves propagating in “pure” liquid, the velocity of detonation soliton may significantly increase compared to the case of one-dimensional bubble detonation.     

The non-linear evolution of modulated waves in a boundary layer

The series of experiments by Schubauer and Skramstad (1948) provided the first experimental evidence of the role that the instability of Tollmien-Schlichting waves played in the transition of a zero pressure-gradient flat plate boundary layer. The initial experiments studied the oscillations in the boundary layer excited by the freestream fluctuations. This was only possible after the background disturbances in the wind tunnel had been reduced to a very low level. The background wind tunnel environment excited a broad band of amplitude modulated disturbance waves that grew as they propagated downstream, eventually leading to the formation of turbulent spots. Further experiments used artificial two-dimensional harmonic excitation to produce regular wavetrains that could be directly compared with linear theory. Unfortunately, two-dimensional harmonic excitation of this type has also been used in many of the subsequent nonlinear transition investigations; the modulation of the disturbance waves, essential in nonlinear studies, has been largely ignored. Gaster and Grant (1975) used a short duration acoustic pulse to excite the boundary layer and found that the modulated wavepacket that was created admitted bursts of high frequency oscillations. These occurred at amplitudes that were insufficient to generate non-linear behaviour in purely periodic wavetrains. Gaster (1980) suggested that the modulation of the wavepacket played an important role in the non-linear region of transition. This investigation used computer generated deterministic white noise to excite the boundary layer on a flat plate through a single buried loudspeaker. This type of excitation produced amplitude modulated T-S waves at some point downstream from the source. By repeatedly exciting the boundary layer with the same white noise sequence it was possible to map the entire flow-field with a single hot-wire probe and so study the evolution of the modulated wavetrains and the eventual development of turbulent spots. The modulated wavetrains were found to grow initially according to linear theory. But downstream, departures from the linear pattern were observed at isolated time instants. The amplitude of the irregular portions of the signal increased rapidly with downstream distance until bursts of oscillations of frequencies five or six times the basic T-S frequency were observed. These regions developed even higher frequency bursts until a turbulent spot could be considered to have formed. Excitation signals of various amplitudes with different phase relations between the spectral components were used in these experiments. It was found that the phases between the Fourier components played an important role in the highly non-linear behaviour that is the precursor to a turbulent spot. Novel signal processing techniques, such as the wavelet transform and Singular Value Decomposition were used to investigate the fine structure and the propagation characteristics of the high frequency disturbances.     

Turbulent boundary layer of water waves near a smooth bottom

Abstract

A one‐layer model describing wave‐induced turbulent flows near a smooth bottom is presented. A time‐invariant effective viscosity model, which is more realistic under natural conditions, is specified near a smooth bottom. The first and second order solutions are presented. These include the velocity profile, shear stress, friction Investigated. These include the velocity profile, shear stress, friction factor and mass transport. The present study simplifies much of the mathematical complexity in many of the existing models. Furthermore, the results compare favorably with available observations, indicating that the approach adopted in the present model is physically sound.     

非周期型理想钻柱系统声传播特性研究

基于一维声传播理论推导出了非周期型理想钻柱系统的频散方程和透射波声衰减方程,数值计算了非周期型钻柱系统几何参量与其频散特性、声衰减特性之间的关系,并利用有限元ANSYS对非周期型理想钻柱系统的声传播特性的结果进行了验证。研究结果表明：非周期型理想钻柱系统的频散特性与多个周期性结构系统频散特性相“与”的结果一致,具有通带较窄而阻带较宽,且频率在阻带范围内的声波沿钻柱传播时声衰减较大的特性。     

Propagation and localization of acoustic and elastic waves in heterogeneous materials: renormalization group analysis and numerical simulations

We describe and discuss the recent progress in the study of propagation and localization of acoustic and elastic waves in heterogeneous media. The heterogeneity is represented by a spatial distribution of the local elastic moduli. Both randomly distributed elastic moduli as well as those with long-range correlations with a nondecaying power-law correlation function, are considered. The motivation for the study is twofold. One is that recent analysis of experimental data for the spatial distribution of the elastic moduli of rock indicated that the distribution is characterized by the type of long-range correlations that we consider in this study. The second motivation for the problem is to understand whether localization of electrons (which, in quantum mechanics, are described by wave functions) has any analogy in the propagation of classical waves in disordered media. The problem is studied by two approaches. One of them is based on developing a dynamic renormalization group (RG) approach to analytical analysis of the governing equations for wave propagation. The RG analysis indicates that, depending on the type of the disorder (correlated vs. uncorrelated), one may have a transition between localized and extended regimes in any spatial dimension. The second approach utilizes numerical simulations of the governing equations in two- and three-dimensional media. The results obtained by the two approaches are in agreement with each other. Using numerical simulations, we also describe how the characteristics of a propagating wave may be used for probing the differences between heterogeneous media with short- and long-range correlations. To do so, we study the evolution of several distinct characteristics of the waves, such as the amplitude of the coherent wave front, its width, the spectral densities, the scalogram (wavelet transformation of the waves’ amplitudes at different scales and times), and the dispersion relation. It is demonstrated that such properties have completely different characteristics in uncorrelated and correlated media. Finally, it is shown how wave propagation may be used for establishing a link between the static and dynamical properties of heterogeneous media.     

Propagation of torsional waves in a viscoelastic layer over an inhomogeneous half space

This paper presents a theoretical study on propagation of torsional surface waves in a homogeneous viscoelastic isotropic layer with Voigt type viscosity over an inhomogeneous isotropic infinite half space. The non-homogeneity in half space is assumed to arise due to exponential variation in shear modulus and density. A closed-form solution has been obtained for the displacement in the layer as well as for a infinite half space. The dispersion and absorption relations for an torsional wave under the assumed geometry have been found. Numerical results are presented for propagation characteristics in terms of a number of non-dimensionalized parameters and have been produced graphically. This study investigates the effect of various parameters, namely non-homogeneity parameter, internal friction, the layer width and complex wave number on dissipation function and phase velocity of the torsional wave. Results in some special cases are also compared with existing solutions available from analytical methods, which show a close agreement.     

Propagation of magnetoelastic shear waves in an irregular self-reinforced layer

The propagation of horizontally polarised shear waves in an internal irregular magnetoelastic self-reinforced stratum which is sandwiched between two semi-infinite magnetoelastic self-reinforced media is studied. Two shapes of irregularities on the interface of layer and lower semi-infinite media are considered, namely rectangular and parabolic. The dispersion equation is obtained in closed form. The combined effects of reinforcement, magnetic field and irregularity are also studied. Some important features of the results are highlighted. It is also observed that the dispersion equation is in agreement with the classical Love-type wave equation for an isotropic layer sandwiched between two isotropic half-spaces in the absence of reinforcement, magnetic field and irregularity.     

Structure of the boundary layer in a stream of a dispersion along a flat plate

The boundary layer in a stream of a dispersion along a flat plate is analyzed on the basis of the particles trajectory near the wall and on the basis of test data.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 4, pp. 646–649, October, 1972.     

Propagation of Rayleigh, Scholte and Stoneley waves along random boundaries

The effect of boundary roughness on the propagation of Rayleigh, Scholte and Stoneley waves is analysed under the assumption of the wavelength being much larger than the roughness scale of the interface. The scattering of the fundamental interface waves is represented by systems of plane waves in both neighbouring half-spaces; the formulas for amplitudes of these waves are determined using the perturbation method. The phase velocity of the interface waves is analysed by an approximate technique and is found to increase with the growing boundary roughness for all three types of interface waves.     

Propagation of thermoelastic acceleration waves in materials with thermal memory

A method of surfaces of discontinuity is used to obtain expressions for velocities and attenuations of thermoelastic waves propagating in a semibounded medium with thermal memory.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 5, pp. 818–825, May, 1986.     

Propagation of Love waves in an elastic layer with void pores

The paper presents a study of propagation of Love waves in a poroelastic layer resting over a poro-elastic half-space. Pores contain nothing of mechanical or energetic significance. The study reveals that such a medium transmits two types of love waves. The first front depends upon the modulus of rigidity of the elastic matrix of the medium and is the same as the love wave in an elastic layer over an elastic half-space. The second front depends upon the change in volume fraction of the pores. As the first front is well-known, the second front has been investigated numerically for different values of void parameters. It is observed that the second front is many times faster than the shear wave in the void medium due to change in volume fraction of the pores and is significant     

Unsteady mixed-convection boundary layer flow along a symmetric wedge with variable surface temperature

Laminar two-dimensional unsteady mixed-convection boundary-layer flow of a viscous incompressible fluid past a sharp wedge has been studied. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations is reduced to local non-similarity boundary layer equations, which are solved analytically for small time. Perturbation solutions are also obtained for small and large dimensionless time, τ. Solutions of the governing equations for all time are obtained employing the implicit finite difference method. Here we have focused our attention on the evolution of skin-friction coefficient (C_f) and local Nusselt number (Nu) (heat transfer rate), fluid velocity and fluid temperature with the effects of different governing parameters such as different time, τ, the exponent, m (=0.2, 0.4, 0.6, 0.8, 1.0), mixed convection parameter, λ (= 0.0, 0.5, 1.0) for fluids having Prandtl number, Pr = 0.1, 0.7, and 7.0.