微管内气泡的受迫振动

在气泡-液柱一维耦合振动模型的基础上对刚性微管两侧声压不相等时管内柱状气泡的轴向一维受迫振动进行了理论探索. 声压不均匀分布不影响气泡线性振动时的共振频率, 但振动幅度受到有效声压幅值的影响. 利用逐级近似法分析了管内非线性振动气泡的基频、三倍频和三分之一分频振动的幅-频响应关系, 结果表明当驱动声压超过0.1 MPa时, 气泡振动处于非线性状态. 非线性声响应特征主要表现为:基频和分频振动幅值响应的多值性; 三倍频振动在低频区响应强于高频区; 三分频振动在大于共振频率的频域内出现的概率更大.     

弹性管中泡群内气泡的非线性声响应

将弹性管壁视为膜弹性结构,得到了管径较大弹性管中泡群内气泡弱非线性振动的动力学模型.利用逐级近似法对气泡的非线性共振频率、基频振动响应特性进行了理论分析.结果表明:气泡共振频率主要受泡群内气泡间相互作用的影响;气泡的非线性共振频率将发生偏移,其偏移量取决于共振响应振幅;气泡的声响应区存在最大频率值;在声响应的高频率区内声响应幅值有多值性.     

双气泡振子系统的非线性声响应特性分析

对初始半径不同的双气泡振子系统在声波作用下的共振行为和声响应特征进行了分析.利用微扰法分析了双泡系统的非线性共振频率,由于气泡间耦合振动的非线性影响,双泡系统存在双非线性共振频率.倍频共振和分频共振现象的存在使得双泡系统振幅-频率响应曲线有多共振峰,且随着非线性增强,共振区向低频区移动.通过对气泡平衡半径、双泡平衡半径比以及气泡间距的分析发现,耦合作用较强的情形发生在系统共振频率附近、气泡半径比接近1以及气泡间距小于10R_(10)的范围内,同时观察到了此消彼长的现象,充分体现了气泡在声场中能量转换器的特征.     

超声波作用下泡群的共振声响应

从球状泡群气泡动力学方程出发, 考虑泡群间次级声辐射的影响, 得到了声场中两泡群共同存在时气泡振动的动力学方程, 并以此为基础探讨声波驱动下双泡群振动系统的共振响应特征. 由于泡群间气泡间的相互作用, 系统存在低频共振和高频共振现象, 两不同共振频率的数值与泡群内气泡的本征频率相关. 泡群内气泡的本征频率又受到初始半径、泡群大小和泡群内气泡数量的影响. 气泡自由振动和驱动声波的耦合激起泡群内气泡的受迫振动, 气泡初始半径、气泡数密度和驱动声波频率等都会影响泡群内气泡的振动幅值和初相位. 关键词： 气泡群 共振 声响应 超声空化     

低频超声空化场中柱状泡群内气泡的声响应

本文在气泡群振动模型的基础上,考虑气泡间耦合振动的影响,得到了均匀柱状泡群内振动气泡的动力学方程,以此为基础分析了低频超声空化场中柱形气泡聚集区内气泡的非线性声响应特征.气泡间的耦合振动增加了系统对每个气泡的约束,降低了气泡的自然频率,增强了气泡的非线性声响应.随着气泡数密度的增加,气泡的自然共振频率降低,受迫振动气泡受到的抑制增强.数值分析结果表明:1)驱动声波频率越低,气泡的初始半径越小,气泡数密度变化对气泡最大半径变化幅度的影响越大;2)气泡振动幅值响应存在不稳定区,不稳定区域分布与气泡初始半径、驱动声波压力幅值、驱动声波频率等因素有关.在低频超声波作用下,对初始半径处在1—10μm之间的空化气泡而言,气泡初始半径越小,气泡最大半径不稳定区分布范围越大,表明小气泡具有更强的非线性特征.因此,气泡初始半径越小,声环境变化对空化泡声响应稳定性影响越显著.     

球状泡群内气泡的耦合振动

振动气泡形成辐射场影响其他气泡的运动, 故多气泡体系中气泡处于耦合振动状态. 本文在气泡群振动模型的基础上, 考虑气泡间耦合振动的影响, 得到了均匀球状泡群内振动气泡的动力学方程, 以此为基础分析了气泡的非线性声响应特征. 气泡间的耦合振动增加了系统对每个气泡的约束, 降低了气泡的自然共振频率, 增强了气泡的非线性声响应. 随着气泡数密度的增加, 振动气泡受到的抑制增强; 增加液体静压力同样可抑制泡群内气泡的振动, 且存在静压力敏感区(1–2 atm, 1 atm=1.01325×10⁵ Pa); 驱动声波对气泡振动影响很大, 随着声波频率的增加, 能够形成空化影响的气泡尺度范围变窄. 在同样的声条件、泡群尺寸以及气泡内外环境下, 初始半径小于5 μm 的气泡具有较强的声响应. 气泡耦合振动会削弱单个气泡的空化影响, 但可延长多气泡系统空化泡崩溃发生的时间间隔和增大作用范围, 整体空化效应增强.     

声波激励下管路轴向分布双气泡动力学特性分析

针对基于声学理论的管道气泡检测技术面临的声波作用下的气泡相互作用机理问题,本文基于自由气泡Rayleigh-Plesset模型,通过引入次Bjerknes辐射力,构建能够考虑管道轴向气泡分布的可压缩性双气泡动力学模型.利用四阶龙格库塔方法开展数值计算,对比分析了不同激励声波频率与幅度作用下自由气泡与双气泡模型引起的气泡动力学特征的区别.同时对比了液体可压缩与不可压缩假设引起的气泡动力幅频响应的区别,表明可压缩假设下的次Bjerknes辐射力引起气泡发生受迫振动,不改变气泡的线性共振特征;而不可压缩假设引起气泡间发生强耦合,从而改变气泡系统的线性共振特征.气泡距离直接影响次Bjerknes辐射力大小,导致气泡动力学趋向于非线性振动,与线性振动的频谱特征差别明显.气泡轴向位置的变化引起外界激励声波的变化,从而改变气泡的初始振动特征.初始特征的差异与次Bjerknes辐射力发生耦合作用,影响气泡动力学特征,甚至发生非线性振动.研究表明,小气泡在共振的情况下,与次Bjerknes辐射力发生耦合作用,使得双气泡系统更容易趋向于非线性特征;而大气泡则能够较好地保持线性共振状态.     

非周期二进制/M进制信号激励下非线性系统的非周期共振研究

研究单一非周期二进制或M进制信号激励下一类非线性系统的非周期共振现象及其度量方法,重点探讨了系统参数引起的非周期共振.提出了适用于非周期共振度量的响应幅值增益指标,并结合互相关系数和误码率展开研究.结果发现,互相关系数能够较好地描述系统输出和输入信号之间的同步性及波形相似性但无法刻画信号通过系统后被放大的程度.响应幅值增益能够较好地描述信号通过系统后幅值被放大的程度,但无法反映系统输出和输入信号之间的同步性及波形相似性.非周期共振发生在互相关系数取谷值和响应幅值增益取峰值处,且两种指标曲线反映的共振点相同.误码率在合适的阈值下可以描述系统输出和输入信号之间的同步性以及非周期信号通过系统后被放大的程度,误码率曲线可以直接给出非周期共振的共振区.单一非周期二进制或M进制信号激励下的非线性系统可以发生非周期共振,其共振效果需要综合互相关系数、响应幅值增益、误码率等指标进行度量.     

非线性电容RLC串联电路的主共振研究

研究非线性电容RLC串联电路,应用多尺度法,得到非线性振动系统主共振的一次近似解并进行数值计算,分析电阻、电感、电容和电动势对主共振幅频响应的影响.结果表明:RLC串联电路的主共振响应有跳跃和滞后现象;随着电动势的增加,主共振的振幅和共振区增大;随着电阻的增大,主共振的振幅和共振区减小.     

超声场中空化泡对弹性粒子微流的影响

从声散射基本理论出发,考虑弹性粒子与空化泡之间耦合作用,结合边界条件,推导了弹性粒子外部声流分布,得到了声微流的n=0和n=1模式近似表达式和粒子表面应力分布函数.数值分析结果表明:气泡和弹性粒子之间的耦合作用增加了粒子周围的微流分布与剪应力场分布,特别是微流速度的切向分量.随着两者间距与相对位置的距离增大,粒子与气泡之间相互作用减弱,粒子周围微流幅值减小;当气泡处于共振状态时,粒子周围的微流分布显著增强.粒子表面剪应力场受粒子半径与声场频率影响,当粒子半径与声场频率越大,外部散射声强越强,粒子表面剪应力幅值越大.     

Nonlinear effects in the dynamics of clouds of bubbles

This paper presents a spectral analysis of the response of a fluid containing bubbles to the motions of a wall oscillating normal to itself. First, a Fourier analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear effects in the oscillation of a single bubble in an infinite fluid. This is used in the approximate solution of the oscillating wall problem, and the resulting expressions are evaluated numerically in order to examine the nonlinear effects. Harmonic generation results from the nonlinearity. It is observed that the bubble natural frequency remains the dominant natural frequency in the volume oscillations of the bubbles near the wall. On the other hand, the pressure perturbations near the wall are dominated by the first and second harmonics present at twice the natural frequency while the pressure perturbation at the natural frequency of the bubble is inhibited. The response at the forcing frequency and its harmonics is explored along with the variation with amplitude of wall oscillation, void fraction, and viscous and surface tension effects. Splitting and cancellation of frequencies of maximum and minimum response due to enhanced nonlinear effects are also observed.     

Resonant third harmonic generation of a short pulse laser in plasma by applying a wiggler magnetic field

We examine the effect of wiggler magnetic field on pulse slippage of short pulse laser-induced third harmonic generation in plasma. The process of third harmonic generation of an intense short pulse laser in plasma is resonantly enhanced by the application of a magnetic wiggler. The laser exerts a ponderomotive force at second harmonic driving density oscillations. The second harmonic oscillations coupled with electron velocity at the laser frequency, produces a non-linear current, driving the third harmonic. Third harmonic pulse generates in the fundamental pulse domain. However, the group velocity of the third harmonic wave is greater than the fundamental wave. Hence, the third harmonic pulse saturates strongly and moves forward from the fundamental pulse at shorter distance than the second harmonic pulse.     

Fractional-harmonic components in an acoustical wave in a liquid

The amplitudes and frequencies of the components of the acoustical spectrum of an acoustical wave, generated in a non-viscous liquid filling a cavity, are calculated by solving a boundary value problem. Apart from forced oscillations, the frequencies of the acoustical spectrum are equal to the frequency of the fundamsntal oscillation of the liquid in the cavity and its higher harmonics. If the frequency of the driving acoustical wave coincides with one of these (proper) frequencies, thefractional harmonic components appear. The amplitudes of the component oscillations decrease monotonically as the absolute value of the difference between the frequency of the driving acoustical wave and the frequency of the respective oscillation is increased. The derived relations are compared with the results of some published measurements.     

Acoustic phase conjugation in a three-phase medium

Acoustic phase conjugation is studied in a sandy marine sediment that contains air bubbles in its fluid fraction. The considered phase conjugation is a four-wave nonlinear parametric sound interaction caused by nonlinear bubble oscillations which are known to be dominant in acoustic nonlinear interactions in three-phase marine sediments. Two various mechanisms of phase conjugation are studied. One of them is based on the stimulated Raman-type sound scattering on resonance bubble oscillations. The other is associated with sound interactions with bubble oscillations whose frequencies are far from resonance bubble frequencies. Nonlinear equations to solve the phase conjugation problem are derived, expressions for acoustic wave amplitudes with a conjugate wave front are obtained and compared for various frequencies of the excited bubble oscillations.     

Double-resonance plasmon-driven enhancement of nonlinear optical response in a metamaterial with coated nanoparticles

By means of a simple analytical model, we show the possibility of giant double-resonance enhancement of nonlinear cubic optical response of metamaterial containing layered (coated) nanoparticles with nonlinear dielectric core covered by metallic shell. Such nanoparticles support two surface plasmons of dipole type with different eigenfrequencies depending on volume portion of nonlinear dielectric. We demonstrate that giant enhancement of nonlinearity takes place under condition of double resonance when the fundamental frequency of light wave and its third harmonic simultaneously coincide or close to the frequencies of surface plasmons.     

Forced linear oscillations of microbubbles in blood capillaries

A theoretical investigation of the forced linear oscillations of a gas microbubble in a blood capillary, whose radius is comparable in size to the bubble radius is presented. The natural frequency of oscillation, the thermal and viscous damping coefficients, the amplitude resonance, the energy resonance, as well as the average energy absorbed by the system, bubble plus vessel, have been computed for different kinds of gas microbubbles, containing air, octafluropropane, and perflurobutane as a function of the bubble radius and applied frequency. It has been found that the bubble behavior is isothermal at low frequencies and for small bubbles and between isothermal and adiabatic for larger bubbles and higher frequencies, with the viscous damping dominating over the thermal damping. Furthermore, the width of the energy resonance is strongly dependent on the bubble size and the natural frequency of oscillation is affected by the presence of the vessel wall and position of the bubble in the vessel. Therefore, the presence of the blood vessel affects the way in which the bubble absorbs energy from the ultrasonic field. The motivation of this study lies in the possibility of using gas microbubbles as an aid to therapeutic focused ultrasound treatments.     

Frequency multiplication of microwave radiation in a semiconductor superlattice by electrons capable to perform Bloch oscillations

We report the observation of frequency multiplication of microwave radiation in a GaAs/AlAs semiconductor superlattice at room temperature. We observed, for a fundamental frequency of 9 GHz, second and third harmonic generation. We associate the harmonic generation with a nonlinear current-voltage characteristic that is determined by Bloch oscillations of electrons propagating along the superlattice axis. Our results suggest for the frequency multiplication an upper limit in the tetrahertz frequency range.