谐振管内非线性驻波的有限体积数值算法

为了扩展谐振管内非线性驻波在工程中的应用, 以及克服现有数值计算方法仅局限于求解直圆柱形和指数形谐振管内非线性驻波的问题. 根据变截面的非稳态可压缩热黏性流体Navier-Stokes方程和空间守恒方程, 并基于求解压力速度耦合方程的半隐式算法和交错网格技术, 构建一种能够计算任意形状轴对称谐振管受活塞驱动时内部非线性驻波的有限体积算法. 分别对圆柱形、指数形和圆锥形谐振管内的非线性驻波进行仿真计算. 通过与现有试验结果以及数值仿真结果的对比, 验证了该方法的正确性.并获得除驻波声压之外的另外一些新的物理结果, 包括速度、密度、温度的瞬时变化.在直圆柱形谐振管内产生冲击声压波, 速度波形中出现钉状结构.而在指数形和圆锥形谐振管内产生高声压幅值的驻波, 没有出现冲击波, 速度波形中均未发现钉状结构. 计算结果表明谐振管内非线性驻波的物理属性与谐振管形状之间有密切关系.     

Nonlinear optical diffraction by standing acoustic waves in a GaAs film

Second-order nonlinear optical diffraction by standing acoustic waves in a crystalline plate is theoretically investigated. A detailed analysis of the polarization state of the second-harmonic light diffracted by both longitudinal and transversal acoustic waves is carried out. It is shown that longitudinal standing acoustic waves only allow p-polarized nonlinear optical diffraction, irrespective of the incoming state of polarization, whereas transversal standing acoustic waves allow all possible combinations of incoming and diffracted polarization states. Numerical estimates of the relative intensities of nonlinearly diffracted radiation peaks are made for a GaAs plate.     

闭管中大振幅驻波理论

大振幅驻波理论现扩展至计入闭管中附面层损耗时的情况.如前,以质点位移表达非线性波相速应计入质点速度的规律.符合驻波中各参量只在原地随时间作交流变化的现象.所得解完全满足流体动力学方程.把声场参量分解为频率分量时所遇到特殊情况做了讨论和处理.也提出一些新现象.     

Nanoscale self-organization using standing surface acoustic waves

The diffusion of an adatom on a substrate submitted to a standing surface acoustic wave is theoretically studied. By performing large scale molecular dynamic simulations, we show that the wave dynamically structures the substrate by encouraging the presence of the adatom in the vicinity of the maximum displacements of the substrate. Using an analytical model, we explain this feature introducing an effective potential induced by the wave. Applied in an atomic deposition experiment, this dynamic structuring process should govern the nucleation sites distribution opening the route to accurately control the self-organization process at the nanoscale.     

周期镶嵌亥姆霍兹共鸣腔平板的声全背向反射

研究斜入射声波在周期镶嵌亥姆霍兹共鸣器的刚性界面上的反射行为。共鸣器间的空间周期间隔d和入射声波的波长λ相当,且大于共振腔尺寸,因此可被视为具有集总参数的声学元件。理论分析和数值计算均表明,当入射波频率和方向既满足布拉格共振条件又同时满足亥姆霍兹共振条件时,在通常的反射方向上反射声波消失,反射波逆入射方向传播,引起与常规反射全然不同的全背向反射。     

Nonlinear thickness-stretch vibration of thin-film acoustic wave resonators

We perform a theoretical analysis on nonlinear thickness-stretch free vibration of thin-film acoustic wave resonators made from AlN and ZnO. The third-order or cubic nonlinear theory by Tiersten is employed. Using Green’s identify, under the usual approximation of neglecting higher time harmonics, a perturbation analysis is performed from which the resonator frequency-amplitude relation is obtained. Numerical calculations are made. The relation can be used to determine the linear operating range of these resonators. It can also be used to compare with future experimental results to determine the relevant thirdand/or fourth-order nonlinear elastic constants.     

Finite-amplitude standing acoustic waves in a cubically nonlinear medium

The acoustic field in a resonator filled with a cubically nonlinear medium is investigated. The field is represented as a linear superposition of two strongly distorted counterpropagating waves. Unlike the case of a quadratically nonlinear medium, the counterpropagating waves in a cubically nonlinear medium are coupled through their mean (over a period) intensities. Free and forced standing waves are considered. Profiles of discontinuous oscillations containing compression and expansion shock fronts are constructed. Resonance curves, which represent the dependences of the mean field intensity on the difference between the boundary oscillation frequency and the frequency of one of the resonator modes, are calculated. The structure of the profiles of strongly distorted “forced” waves is analyzed. It is shown that discontinuities are formed only when the difference between the mean intensity and the detuning takes certain negative values. The discontinuities correspond to the jumps between different solutions to a nonlinear integro-differential equation, which, in the case of small dissipation, degenerates into a third-degree algebraic equation with an undetermined coefficient. The dependence of the intensity of discontinuous standing waves on the frequency of oscillations of the resonator boundary is determined. A nonlinear saturation is revealed: at a very large amplitude of the resonator wall oscillations, the field intensity in the resonator ceases depending on the amplitude and cannot exceed a certain limiting value, which is determined by the nonlinear attenuation at the shock fronts. This intensity maximum is reached when the frequency smoothly increases above the linear resonance. A hysteresis arises, and a bistability takes place, as in the case of a concentrated system at a nonlinear resonance.     

The diffraction of light at ultrasonic waves in acoustic resonators

A theoretical treatment is given of the diffraction of light by hypersonic waves excited in solid prismatic samples. For a fixed frequency, a set of modes exists in such a resonator. The modes differ in the spatial distribution of the field, which corresponds to a set of partial waves propagating over an entire solid angle. The diffraction occurs only at the partial waves which satisfy the Bragg condition and the diffraction pattern has the form of a circle consisting of a large number of points. An expression is found for the angular separation of adjacent points which correspond to different modes. It is shown experimentally that for the scattered light field in the far zone the diffraction patterns are similar to Shaefer-Bergmann patterns. Explanations are given for the shape and fine structure of these patterns. The structure of the diffracted light beams in the near zone is also studied and the frequency intervals between the excitation of the various resonator modes are measured. The experimental results are in qualitative agreement with the theory.     

Nonlinear standing waves in a resonator with feedback control

An experimental study is presented to demonstrate that nonlinear effect on standing waves in a resonator can be reduced by a feedback loop responding to the second harmonic. The resonator was a cylindrical tube sealed at one end and driven by a horn driver unit at another end. The feedback control loop consisted of a pressure sensor, a frequency filter, a phase shifter, and an actuator. The results show that the waveform distortions can be eliminated and large amplitude sinusoidal pressure oscillations are obtained. A simple model is proposed for a qualitative discussion on the control mechanism, which shows that the feedback loop alters the imaginary part of the complex mode frequency so as to suppress (or enhance) the second harmonic.     

Nonlinear evolution of 3D drift-ion-sound standing waves

Temporal evolution of coupled drift-ion-sound standing wave is considered. Perturbation theory based on the multiple-time-scale formalism is built. Nonlinear effects up to the third order in amplitude are discussed.     

Nonlinear electron density waves and nonlinear acoustic waves in carbon nanotubes

Problems in nonlinear properties of carbon nanotubes with a strong interaction of electrons are considered if the electron mobility, the Coulomb repulsion of electrons at one site of a carbon nanotube, and variations in the distance between neighboring sites owing to acoustic oscillations are taken into account. The possible occurrence of nonlinear acoustic lattices in carbon nanotubes that are small in diameter is investigated.     

Nonlinear ultrasonic standing waves: two-dimensional simulations in bubbly liquids

We present the results of numerical predictions for analyzing the behavior of nonlinear ultrasonic standing waves in two-dimensional cavities filled with bubbly liquids. The model we solve accounts for nonlinearity, dissipation, and dispersion of the two-dimensional media due to the bubbles. The numerical simulations are based on a finite-difference scheme. They consider the bubbles evenly distributed in the liquid. Results are shown for high-amplitude signals. They make it possible to observe how the linear modes turn into multi-frequency nonlinear fields.     

Resonant interaction of standing acoustic waves with a spin system

A theory is developed of the reaction of a spin system to a resonant action of an acoustic field and an electromagnetic field. It is shown that it is important to allow for the coherent properties of the acoustic field that excites the spin system both for the calculation of the line profile of direct acoustic absorption and for the line profile of saturation of paramagnetic resonance by sound. By studying the influence of the acoustic field on the profile of the absorption line of rf power it becomes possible to determine the magnitude and sign of the spin-phonon interaction constant.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 77–81, October, 1973.We are very grateful to V. R. Nagibarov for discussing the work.     

Nonlinear ion acoustic solitary waves in electron-positron-ion inhomogeneous plasma

A theoretical investigation has been made for studying the propagation of ion-acoustic waves (IAWs) in a weakly inhomogeneous, collisionless, unmagnetized, three-component plasmas, whose constituents are inertial ions, nonthermal electrons, and Boltzmannian positrons. Employing reductive perturbation method (RPM), the variable coefficients Korteweg-de Varies equation (KdV) is derived. At the critical ion density, the KdV equation is not suitable for describing the system. Thus, a new set of stretched coordinates is considered to derive the modified variable coefficients KdV equation. Above (below) this critical point the system supports compressive (rarefactive) solitons. The effect of plasma parameters on the soliton profile has been considered. It has been shown that the width and the amplitude of the soliton affected by wave propagation speed, ratio of positron-to-electron density, and nonthermal parameter.     

Nonlinear acoustic waves in a collisional self-gravitating dusty plasma

Using the reductive perturbation method,we investigate the small amplitude nonlinear acoustic wave in a collisional self-gravitating dusty plasma.The result shows that the small amplitude dust acoustic wave can be expressed by a modified Korteweg-de Vries equation,and the nonlinear wave is instable because of the collisions between the neutral gas molecules and the charged particles.     

Nonlinear acoustic waves in channels with variable cross sections

The point symmetry group is studied for the generalized Webster-type equation describing nonlinear acoustic waves in lossy channels with variable cross sections. It is shown that, for certain types of cross section profiles, the allowed symmetry group is extended and the invariant solutions corresponding to these profiles are obtained. Approximate analytic solutions to the generalized Webster equation are derived for channels with smoothly varying cross sections and arbitrary initial conditions.     

Propagation of acoustic waves in a fluid-filled pipe with periodic elastic Helmholtz resonators

Helmholtz resonators are widely used to reduce noise in a fluid-filled pipe system. It is a challenge to obtain lowfrequency and broadband attenuation with a small sized cavity. In this paper, the propagation of acoustic waves in a fluid-filled pipe system with periodic elastic Helmholtz resonators is studied theoretically. The resonance frequency and sound transmission loss of one unit are analyzed to validate the correctness of simplified acoustic impedance. The band structure of infinite periodic cells and sound transmission loss of finite periodic cells are calculated by the transfer matrix method and finite element software. The effects of several parameters on band gap and sound transmission loss are probed.Further, the negative bulk modulus of periodic cells with elastic Helmholtz resonators is analyzed. Numerical results show that the acoustic propagation properties in the periodic pipe, such as low frequency, broadband sound transmission, can be improved.