水下多层均匀材料的声特性

本文研究水和空气中由不同厚度的两层弹性板及消声橡胶共同组成的分层介质在斜入射时的声特性,并采用数值方法求解多层结构声场的线性方程组。得到反射,透射系数,当板的厚度远小于波长时,采用弹性薄壳振动模型和弹性波模型进行计算,它们的结果基本相同,但是薄壳振动模型更便于计算和理论分析;对系统反射系数和透射系数的计算结果表明,系统增加消声橡胶层后,极大地改变后射系数和透射系数的频率响应;频率升高,反射系数减小     

Shear waves in a resonator with cubic nonlinearity

Shear waves with finite amplitude in a one-dimensional resonator in the form of a layer of a rubber-like medium with a rigid plate of finite mass at the upper surface of the layer are investigated. The lower boundary of the layer oscillates according to a harmonic law with a preset acceleration. The equation of motion for particles in a resonator is determined using a model of a medium with a single relaxation time and cubical dependence of the shear modulus on deformation. The amplitude and form of shear waves in a resonator are calculated numerically by the finite difference method at shifted grids. Resonance curves are obtained at different acceleration amplitudes at the lower boundary of a layer. It is demonstrated that, as the oscillation amplitude in the resonator grows, the value of the resonance frequency increases and the shape of the resonance curve becomes asymmetrical. At sufficiently large amplitudes, a bistability region is observed. Measurements were conducted with a resonator, where a layer with the thickness of 15 mm was manufactured of a rubber-like polymer called plastisol. The shear modulus of the polymer at small deformations and the nonlinearity coefficient were determined according to the experimental dependence of mechanical stress on shear deformation. Oscillation amplitudes in the resonator attained values when the maximum shear deformations in the layer were 0.4–0.6, which provided an opportunity to observe nonlinear effects. Measured dependences of the resonance frequency on the oscillation amplitude corresponded to the calculated ones that were obtained at a smaller value of the nonlinear coefficient.     

Instability of a flat horizontal interface between a thin layer of a ferrofluid and a thin layer of a nonmagnetic liquid in the presence of a vertical magnetic field

An asymptotic analysis of the equations and boundary conditions of fluid dynamics is performed, and a nonlinear model is constructed for the onset of the development of Rosensweig instability in a thin horizontal ferrofluid layer at rest covered with a thin layer of a lighter nonmagnetic liquid. The surface of a nonmagnetized slab is the lower boundary of the ferrofluid, and the interface with a gas is the upper boundary of the nonmagnetic liquid. The pressure in the gas is constant. The instability being considered arises upon the application of a rather strong uniform vertical magnetic field. The proposed model involves five dimensionless parameters. The critical magnetization of the initial ferrofluid layer with a flat upper boundary and the threshold wave number are found. The effect of the governing parameters on the instability region and on the wavelength of the fastest growing mode is studied in the linear formulation of the problem.     

Orientation phenomena in nematic liquid crystals under a periodic compressional deformation

The orientation behavior of homogeneous planar layers of nematic liquid crystals with open and closed ends in the field of compressional deformations caused by an acoustic effect is studied. The mechanisms determining the connection of the optical response of a nematic liquid crystal (the variable component of an optical signal and its spectrum) with the acoustic parameters (the oscillation amplitude and frequency, and the amplitude of sound pressure) and the layer thickness are revealed. The factors responsible for the mechanism and modes of acoustooptic conversion are considered. It is demonstrated that, by varying the layer thickness, it is possible to implement different modes of signal conversion. The possibility of designing a new modification of a sound receiver based on a nematic liquid crystal and the specific features of this design are discussed. Its advantages over conventional sound pressure receivers based on nematic liquid crystals are indicated, in particular, the absence of limitation of the frequency of the received signal in the low-frequency range.     

Flows in a rotating elastico-viscous fluid induced by torsional oscillations of a plate acting for a finite time

Unsteady flows in an electrically conducting rotating elastico-viscous liquid in the presence of a uniform magnetic field and induced by small amplitude torsional oscillations, acting for a finite time, of an infinite, rigid, non-conducting plate, are discussed. This analysis indicates the general features of the steady and unsteady velocity field, and the structure of the associated boundary layers on the plate including the effect of rotation, hydromagnetic and elastic parameters involved in the problem. The velocity field related to small elastic parameter is calculated with physical significance. It is further shown that the Ekman suction velocity, which is responsible for the generation of an axial inflow toward the bounadry layer, does not appear unless the plate is subject to oscillations for an indefinite period. Several limiting results are found to follow as special cases of this analysis.     

Polymer elasticity-driven wrinkling and coarsening in high temperature buckling of metal-capped polymer thin films

We report the critical effects the deformational stress from the elastic nature of a confined polymer layer has during the relaxation process on the buckling of thin metal-polymer bilayer systems (less than 100 nm) even above the temperature at which the polymer is in the liquid flow region. In contrast with what is generally believed, the dispersion force does not play a significant role in the buckling. We also find that the final wrinkled waves take on the shape of wormlike islands. The coarsening leading to the island structure is driven by the growth in amplitude of the dominant wave at the expense of less dominant ones.     

Non-linear flexural waves in thin layers

Non-linear flexural waves in thin plates or layers have been analyzed in this paper. The equation of motion of the plate is derived assuming that the motion is antisymmetric about the mid-plane of the plate and that the plate is thin. The plate is considered to be elastic. The Von Karman non-linear strains and Landau elastic constants have been used to model geometric and material non-linearities, respectively. An asymptotic analysis of wave motion is presented using the method of multiple scales. Evolution equations are derived for small amplitude traveling flexural elastic waves. Numerical results show waveform distortion, amplitude amplification, and harmonic generation.     

Two-dimensional analysis of the effect of an electrode layer on surface acoustic waves in a finite anisotropic plate

The effect of a metal layer over an elastic substrate on surface acoustic wave propagating in the structure can be evaluated precisely for semi-infinite solids and infinite plates, but there is no accurate analytical solution if the finite size of the plate has to be considered. By expanding displacements with eigensolutions of surface acoustic waves in a semi-inifite solid, a set of two-dimensional equations similar to the Mindlin plate theory are obtained. Then for a thin electrode layer, the effect is considered through the approximation of displacements in the metal layer with the ones in the substrate, and an integration over the thickness incorporated the properties of the metal layer into equations through the modification of material properties with the decaying indices of surface acoustic waves and the thickness of the metal layer. Using AT-cut quartz crystal as the substrate, we present the effect of silver electrode layers of finite thickness on the phase velocity of propagating surface acoustic waves.     

Experimental and Theoretical Study of Sprays Produced by Ultrasonic Atomisers

The atomisation of liquids by means of low-frequency ultrasonic atomisers results from unstable surface waves generated on the free surface of a thin liquid film. These unstable waves are obtained from the tuning of the amplitude and the frequency of an imposed oscillation. The thin liquid film develops as the liquid spreads over the atomising surface of the atomiser. This paper focuses on a systematic experimental analysis of the sprays produced by low-frequency ultrasonic atomisers. The thickness of the liquid film was measured and its effects on the drop diameter were studied together with the effects of both the liquid's physical properties and the ultrasonic atomiser's characteristics. The relationship between the mean drop diameter and the surface wave wavelength was accurately determined and introduced into a mathematical approach based on the maximum entropy formalism to predict the drop size distribution of the spray. Within the range of working conditions tested, the application of this formalism is successful and provides a procedure for the prediction of spray drop size distributions from calculations only.     

On the structure of the velocity field under the free spheroidal surface of a viscous liquid drop oscillating in an electrostatic field

An asymptotic analytical solution to an initial boundary-value problem considering (i) the time evolution of the capillary oscillation amplitude as applied to a viscous spheroidal liquid drop placed in a uniform electrostatic field and (ii) the liquid flow velocity field inside the drop is found. The problem is solved in an approximation that is linear in two small parameters: the dimensionless oscillation amplitude and the dimensionless field-induced constant deformation of the equilibrium (spherical) shape of the drop. Terms proportional to the product of the small parameters are retained. In this approximation, interaction between oscillation modes is revealed. It is shown that the intensity of the eddy component of the oscillation-related velocity field depends on the liquid viscosity and the external uniform electrostatic field strength. The intensity of the eddy component decays rapidly with distance from the free surface. The depth to which the eddy flow (which is caused by periodical flows on the free surface) penetrates into the drop is a nonmonotonic function of the polar angle and increases with dimensionless viscosity and field strength.     

Nonlinear resonance interaction between the oscillation modes of a spherical liquid layer on the surface of a melting hailstone

Evolutionary equations are derived and solved that describe the time dependence of the oscillation mode amplitudes on the surface of a charged conducting liquid layer resting on a solid core. It is assumed that the layer experiences a multimode initial deformation. The equations are solved asymptotically in the second order of smallness in the small dimensionless amplitude of capillary oscillations on the surface of the layer. Mechanisms behind internal nonlinear resonance interaction between the modes of the liquid layer oscillations and behind energy transfer between the modes both in degenerate and in secondary combination resonances are investigated. It is found that in the degenerate resonance interaction between oscillation modes, the energy may be transferred not only from lower to higher modes but also vice versa if the higher mode is excited at the zero time. This conclusion is valid not only for a liquid layer on the surface of a solid core but also for a drop.     

Oscillation of the convective flow around an air bubble in a vertically stratified surfactant solution

The appearance of oscillatory modes of the concentration convection around an air bubble in an aqueous solution with a vertical gradient of surfactant concentration was revealed experimentally. The solution filled a thin vertical layer containing an air bubble in the form of a short horizontal cylinder with a free lateral surface. Due to a small layer thickness, two-dimensional flows and concentration distributions were generated in the liquid. Their evolution was investigated using an interferometric technique. It was found that the flow oscillation was caused by a specific interaction between the diffusion and two solutal (capillary and gravitational) mechanisms of convective mass transfer, which had quite different characteristic times. The time variation of the oscillation period was analyzed in relation to the surfactant concentration gradient, the average solution concentration, and the concentration Marangoni number. It was shown that the ratio of the dimensionless oscillation frequency to the Marangoni number is time independent and is the same for different liquids and various orientations of the concentration gradient. Published in Russian in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2006, Vol. 130, No. 2, pp. 363–370. The text was translated by the authors.     

Shock wave emission from laser-induced cavitation bubbles in polymer solutions

The role of extensional viscosity on the acoustic emission from laser-induced cavitation bubbles in polymer solutions and near a rigid boundary is investigated by acoustic measurements. The polymer solutions consist of a 0.5% polyacrylamide (PAM) aqueous solution with a strong elastic component and a 0.5% carboxymethylcellulose (CMC) aqueous solution with a weak elastic component. A reduction of the maximum amplitude of the shock wave pressure and a prolongation of the oscillation period of the bubble were found in the elastic PAM solution. It might be caused by an increased resistance to extensional flow which is conferred upon the liquid by the polymer additive. In both polymer solutions, however, the shock pressure decays proportionally to r⁻¹ with increasing distance r from the emission centre.     

Electronic Bloch oscillation in a pristine monolayer graphene

In a pristine monolayer graphene subjected to a constant electric field along the layer, the Bloch oscillation of an electron is studied in a simple and efficient way. By using the electronic dispersion relation, the formula of a semi-classical velocity is derived analytically, and then many aspects of Bloch oscillation, such as its frequency, amplitude, as well as the direction of the oscillation, are investigated. It is interesting to find that the electric field affects the component of motion, which is non-collinear with electric field, and leads the particle to be accelerated or oscillated in another component.     

金属薄板弹性各向异性检测

当平面声波入射到液体中的金属薄板上时，透射系数将随声波入射角变化，根据这一规律，能够准确地测定声波入射面与金属薄板交线方向上金属板材料的弹性常数，测得金属薄板面内不同方向的弹性常数，对金属薄板弹性各向异性情况将有一清蜥的认识，由于测试过程采用微机控制、数据采集和处理，实现了各向异性测量的全自动化，该方法测试时间短、所需样品小且加工方便，并可测试金属薄板弹性各向异性的均匀度。     

Excitation of seismoacoustic waves by a harmonic force source acting at the boundary of a liquid layer and an elastic halfspace

A problem on the excitation of seismoacoustic waves in a system of a homogeneous isotropic elastic halfspace covered with a liquid layer is solved in the case of action of a source of point harmonic force on the surface of an elastic medium. Integral expressions are obtained for the radiation powers averaged over a wave period for longitudinal and transverse waves in a solid. Mode excitation is analyzed in detail. Expressions describing parts of the mode powers radiated into a liquid layer and an elastic medium are obtained. Numerical analysis of radiation powers is conducted for spherical longitudinal and transverse waves as well as for the radiation powers of seismoacoustic modes in a solid halfspace and a liquid layer. It is determined that in the conditions characteristic of bottom rocks in the case, where the basin depth is several times and more larger than the sound’s wavelength, about 2/3 of the total power is radiated into a liquid.     

Optical multilayer post growth instabilities: Analyses of Gd2O3/SiO2 system in combination with scanning probe force spectroscopy

Post growth multilayer instabilities of a certain periodic Gd₂O₃/SiO₂ multilayer systems have been investigated using scanning probe force-distance spectroscopy and optical spectrophotometric techniques. In the present work, we have noticed a strong correlation between the force spectroscopic results and the spectral properties of multilayer thin films, although measurement techniques and operating principles are quite different. From the experimental analysis, it was quite evident that the instability process, which starts during the nucleation and growth stage in thin films, continues to persist at a much longer time scale under post growth conditions. During this study it has been noticed that the elastic properties of the constituent thin films, the layer geometry and the bilayer thickness have strong correlation in trickling the multilayer instabilities. Such aspects also have strong interconnections with the morphological and viscoelastic changes. It is also noticed that most of the instabilities results cannot only be explained through elastic nature of the material alone. Instead, total number of layers, the layer structures, morphological changes, corresponding stiffness and the adhesion properties of the multilayer contribute substantially to these phenomena.     

Resonance oscillation damping of a scanning microscope probe by a near-surface viscous liquid layer

Viscous liquid layer motion between a probe with a tip shaped as a paraboloid of revolution and a surface is considered for semicontact-mode operation of a scanning probe microscope. The presence of a viscous liquid layer leads to energy dissipation and is one of the factors responsible for the decrease in the probe oscillation amplitude. The Reynolds equation for viscous liquid motion is used to obtain an analytic solution to the problem. The formula derived for the loss is compared with experimental data obtained for probes and layers with various curvature radii and viscosities.     

On the thickness of a boundary layer related to the oscillating free surface of a charged drop of a viscous liquid

The capillary oscillations of a charged drop of a viscous liquid are calculated in terms of the boundary layer theory in an approximation linear in oscillation amplitude. Calculation is accompanied with the estimation of a relative error that arises when the exact solution is replaced by an approximate one. It is shown that, for the calculation accuracy in the framework of the boundary layer theory to be about several percent, the thickness of the boundary layer near the free surface of the drop must be several times larger than that at which the intensity of the eddy flow caused by the oscillating surface decreases by e times. As the viscosity of the liquid grows, so does the thickness of the boundary layer.     

Study of interactions between liquid vortices and bubbles by simultaneous particle image velocimetry and laser-induced fluorescence tracking

Extensive experimental research has been conducted using the particle image velocimetry (PIV), laser-induced fluorescence (LIF) imaging and backlit photographic recordings to study the complex interactions between coherent vortex structures created in the shear layer of jets and the bubbles. Triggering of the naturally-developing instabilities of the shear layer by a thin, pulsed annular flow surrounding the jets allowed the creation of large, orderly structures with controllable frequency and phase. Synchronization of the triggering with data acquisition permitted phase averaging of the data and revealed several interesting phenomena. In particular, the evolution of large vortices and bubble fields could be tracked and the interactions could be studied. The horizontal and vertical velocity components of the liquid and bubble fields and the vertical velocity of both the vortex and bubble rings that were created were measured by the PIV. LIF and image recordings have been combined to visualize bubble trapping inside large eddy structures.