Free vibration of a spherical liquid drop attached to a conical base in zero gravity

Free vibration analysis of a spherical liquid drop attached to a conical base is presented. Assuming the liquid is incompressible and inviscid, and introducing a velocity potential, axisymmetric and asymmetric vibration characteristics are clarified, considering two liquid contact conditions: slipping edge and anchored edge. In the numerical calculations, for a wide range of conical base apex angles, the natural frequency and vibration mode of a liquid drop are presented. From these parameters, the vibration characteristics of a liquid drop attached to a conical base with general apex angle can be easily predicted. When the apex angle tends to 180°, natural frequencies are found to converge to those of a spherical drop under both slipping and anchored edge conditions, except in the axisymmetric mode with meridian mode number m=0 in the anchored edge case and asymmetric mode m=1 and n=1 in the slipping edge case.     

On the capillary vibration and stability of a charged bubble in a dielectric liquid

The capillary vibration and stability of a charged bubble against infinitesimal volume and shape perturbations when the bubble is immersed in a viscous incompressible dielectric liquid are studied. The range of physical parameters where the noncentrosymmetric radial and axisymmetric surface motions of the bubble are unstable is found. Asymptotic analytical expressions for the damping constant of the axisymmetric capillary vibration in the low-and high-viscosity approximations are derived.     

Forced flexural vibrations of a pipe with a liquid flow

The effect of a liquid flow on the forced vibrations of a pipe under an external driving force is studied both theoretically and experimentally. The analytic dependences of the displacement field on the frequency, the liquid flow velocity, the force application point, and the parameters of the pipe and the liquid are determined by means of the small perturbation method. Experimental results agree well with theoretical dependences. It is shown that the effect of the liquid flow on the pipe vibrations is maximal in the vicinity of the resonance of the second vibration mode.     

方波电泳电场驱动下液膜马达的电致流动特征

液膜马达作为一种新颖的实验装置在基础研究和技术应用方面都将会发挥着重要的作用, 深入研究各种条件下液膜马达的电致流动特征是非常有意义的. 本文从理论上研究了均匀恒定外电场中的液膜马达在方波电泳电场驱动下的动力学特征, 解析地给出了液膜转动的线速度随时空变化的规律. 理论结果表明, 液膜会随着电泳电场频率的增大由对称性往复转动逐渐转变为振动, 这不仅有助于从理论上认识液膜马达振动的物理根源, 也为在实际应用中设计液膜搅拌机提供了一种新思路.     

Analyses of vibration responses on nanoscale processing in a liquid using tapping-mode atomic force microscopy

An analytical solution of the vibration responses of biological specimens using atomic force microscopy (AFM), which often requires operation in a liquid, is developed. In this study, the modal superposition method is employed to analyze the vibration responses of AFM cantilevers in tapping mode (TM) operated in a liquid and in air. The hydrodynamic force exerted by the fluid on AFM cantilevers is approximated by additional mass and hydrodynamic damping. The tip–sample interaction forces were transformed into axial, distributed transversal, and bending loading, and then applied to the end region of the AFM through the tip holder. The effects of transverse stress and bending stress were adopted to solve the dynamic model. With this model, a number of simulations were carried out to investigate the relationship between the transient responses of the cantilever in a liquid and the parameters considered in nanoscale processing. The simulations show that the vibration of AFM cantilevers in a liquid has dramatically different dynamic characteristics from these of that in air. The liquid reduces the magnitude of the transversal response and reduces the cantilever resonances. Moreover, the magnitudes of response become larger with increasing intermolecular distances and smaller with decreasing tip length. The cantilever vibration amplitudes significantly depend on the damping constant and the mass proportionality constant.     

Damping effect of an external uniform magnetic field on gas bubble vibration in a viscous conductive liquid

Dynamic and heat-transfer processes accompanying the free vibrations of a gas bubble immersed in a viscous conductive liquid exposed to a uniform magnetic field are considered. Solutions to a set of equations describing bubble relaxation are obtained by numerical methods. It is shown that the magnetic field causes the fast damping of the vibration due to Joule dissipation. At the stage of vibration, the energy dissipates mainly through the Joule mechanism. At the final stage, thermal dissipation prevails.     

径向极化压电陶瓷长圆管复合超声换能器的径向振动

提出了一种圆管式径向复合压电陶瓷换能器,并对其径向振动特性进行了分析。该换能器由径向极化的压电陶瓷圆管以及金属外圆管组成。利用解析法得出了金属圆管以及具有任意壁厚的径向极化压电陶瓷圆管径向振动的机电等效电路。基于金属圆管与压电圆管的机械边界条件,得出了换能器的六端机电等效电路。在此基础上得出了换能器共振及反共振频率方程的解析表达式,给出了换能器的共振及反共振频率与其几何尺寸之间的依赖关系。利用数值方法对换能器的径向振动特性进行了模拟及仿真,并与解析结果进行了比较。最后,设计并加工了一些径向复合管式压电陶瓷换能器,利用精密阻抗分析仪对其共振及反共振频率进行了实验测试。研究结果表明,利用解析理论得出的换能器共振及反共振频率与数值模拟结果以及实验测试结果符合很好。      

On nonlinear vibrations of a charged drop in the third-order approximation in the amplitude of initial single-mode excitation

Nonlinear axisymmetric motions of the free surface of a charged drop of an ideal liquid under the single-mode initial deformation of its equilibrium shape is investigated in the third-order approximation in the initial perturbation amplitude. An analytical expression for the drop shape generatrix is derived. Nonlinear corrections to the vibration frequencies for the initial perturbation of an arbitrary mode are found for the first time. The effect of vibration nonlinearity on the instability of the drop against its self-charge is studied.     

Modelling and dynamic properties of a novel solid and liquid mixture vibration isolator

Solid and Liquid Mixture (SALiM) vibration isolator is a new isolator which is designed for vibration isolation of heavy equipment with low frequency. The isolator contains liquid and elastic solid elements as working media. To get the stiffness property of the isolator, this paper establishes the mechanics model of elastic solid elements by introducing plate-shell model. Considering geometry nonlinearity, the stiffness of the element under outer liquid pressure and inner air pressure was obtained by perturbation method. Then the stiffness of isolator is derived. As a result, the stiffness is piecewise linear-nonlinear and determined by parameters of the elastic elements and elastic container. In addition, the equation of motion (EOM) of a single degree of freedom system supported by a SALiM isolator is given. The properties of the frequency response function (FRF) of the system are analysed using averaging method which is a classical approximation approach for estimating nonlinear system FRF. And it is found that the system with SALiM isolator shows softening stiffness behaviour. The jumping phenomenon clearly occurs under certain condition. Finally, the vibration isolation property is predicted based on energy transmissibility (ET) in different cases.     

On the calculation of the translational mode amplitude for a drop nonlinearly vibrating in an environment

The second-order amplitudes of the capillary vibration modes of a drop of an ideal incompressible liquid placed in an incompressible ideal medium are calculated. The approximation is quadratic in initial multimode deformation of the equilibrium spherical shape caused by nonlinear interaction. The mathematical statement of the problem is such that the immobility condition for the center-of-mass of the drop is met automatically. When the translational mode amplitude is calculated, a set of hydrodynamic boundary conditions at the interface, rather than the condition of center-of-mass immobility (which is usually applied for simplicity in the problems of drops vibration in a vacuum), should be used.     

Dynamic responses of a pair of circular tubes subjected to liquid cross flow

This paper presents the results of two experimental investigations of a pair of circular tubes subjected to liquid cross flow: (1) two tubes in a plane normal to the flow stream; and (2) two tubes in tandem. Tube response characteristics, including natural frequencies, damping, displacements and vibration orbits, are measured and reported. Results of this study provide additional insight into the interaction of pairs of tubes in liquid flow, including such phenomena as flow velocity-dependent damping and the frequency “lock-in” region of tube motion in the drag direction.     

On acoustic radiation from a nonlinearly vibrating charged drop

An expression for the time-varying shape of an incompressible liquid drop immersed in a compressible dielectric medium is derived to the second-order approximation in drop vibration amplitude. It is shown that the acoustic radiation spectrum of the drop has a monopole component, which makes a considerable contribution to the integral radiation intensity. Its appearance is associated with the time variation of the zeroth-mode vibration amplitude, showing up in the second order of smallness.     

Radial vibration and ultrasonic field of a long tubular ultrasonic radiator

The radial vibration of a metal long circular tube is studied analytically and its electro-mechanical equivalent circuit is obtained. Based on the equivalent circuit, the radial resonance frequency equation is derived. The theoretical relationship between the radial resonance frequency and the geometrical dimensions is studied. Finite element method is used to simulate the radial vibration and the radiated ultrasonic field and the results are compared with those from the analytical method. It is concluded that the radial resonance frequency for a solid metal rod is larger than that for a metal tube with the same outer radius. The radial resonance frequencies from the analytical method are in good agreement with those from the numerical method. Based on the acoustic field analysis, it is concluded that the long metal tube with small wall thickness is superior to that with large wall thickness in producing radial vibration and ultrasonic radiation. Therefore, it is expected to be used as an effective radial ultrasonic radiator in ultrasonic sewage treatment, ultrasonic antiscale and descaling and other ultrasonic liquid handling applications.     

液体对微振动的放大效应

根据表面波声光效应的原理,实验上建立了固体表面微振动的激光衍射测量系统.当激光斜入射到微振动引起的液体表面波上,观察到了清晰、反衬度非常高的衍射图样.利用MATLAB软件对拍摄的衍射图样进行扫描,得到了衍射光斑的光强分布图,并根据衍射图样宽度与表面波振幅的解析关系式,求出了液体表面波的振幅,其大小在微米量级.改变样品池中液体的深度,测得不同深度下液体表面波的振幅,给出了表面波振幅与液体深度之间的解析关系,并发现了液体对微振动的放大效应.利用液体对微振动的放大效应,求出了固体表面微振动的振幅,实现了固体表面微振动的探测.     

液体对微振动的放大效应

根据表面波声光效应的原理,实验上建立了固体表面微振动的激光衍射测量系统.当激光斜入射到微振动引起的液体表面波上,观察到了清晰、反衬度非常高的衍射图样.利用MATLAB软件对拍摄的衍射图样进行扫描,得到了衍射光斑的光强分布图,并根据衍射图样宽度与表面波振幅的解析关系式,求出了液体表面波的振幅,其大小在微米量级.改变样品池中液体的深度,测得不同深度下液体表面波的振幅,给出了表面波振幅与液体深度之间的解析关系,并发现了液体对微振动的放大效应.利用液体对微振动的放大效应,求出了固体表面微振动的振幅,实现了固体表面微振动的探测.     

Vibration characteristics of aluminum surface subjected to ultrasonic waves and their effect on wetting behavior of solder droplets

The vibration characteristics of an aluminum surface subjected to ultrasonic waves were investigated with a combination of numerical simulation and experimental testing. The wetting behavior of solder droplets on the vibrating aluminum surface was also examined. The results show that the vibration pattern of the aluminum surface is inhomogeneous. The amplitude of the aluminum surface exceeds the excitation amplitude in some zones, while the amplitude decreases nearly to zero in other zones. The distribution of the zero-amplitude zones is much less dependent on the strength of the vibration than on the location of the vibration source. The surface of the liquid solder vibrates at an ultrasonic frequency that is higher than the vibration source, and the amplitude of the liquid solder is almost twice that of the aluminum surface. The vibration of the surface of the base metal (liquid solder) correlates with the oxide film removal effect. Significant removal of the oxide film can be achieved within 2 s when the amplitude of the aluminum surface is higher than 5.4 μm or when the amplitude of the liquid solder surface is higher than 10.2 μm.     

Autoparametric resonance in a structure containing a liquid,Part I: Two mode interaction

An elastic structure carrying a rigid circular cylindrical tank containing a liquid with a free surface is considered. Autoparametric coupling between a single structural freedom and the first antisymmetric sloshing mode is investigated theoretically and experimentally. Under the condition of principal internal resonance (i.e., when the structure natural frequency equals twice the liquid sloshing frequency) the response of the system is obtained by an asymptotic approximation taken to the second order. Both theoretical and experimental results show that the coupling between liquid sloshing and vertical structure vibration is rather weak.     

Nonlinear capillary vibrations of a charged drop placed in a dielectric medium: Single-mode initial deformation of the drop shape

The nonlinear vibrations of the equilibrium spherical shape of a charged drop placed in a perfect incompressible dielectric medium are asymptotically calculated in the second-order approximation in single-mode initial deformation of the drop surface. The drop is assumed to be a perfect incompressible liquid. It is shown that the nonlinear vibration amplitudes, as well as the energy distribution between nonlinearly excited modes, depend significantly on the parameter ρ, where ρ is the ratio of the environmental density to that of the drop. It is also demonstrated that an increase in ρ raises the amplitude of the highest of the vibration modes excited due to second-order nonlinear interaction. In the second order of smallness, the amplitude of the zeroth mode is independent of the density ratio. As ρ grows, the effect of the self-charge of the drop, the interfacial tension, and the permittivity of the environment on the nonlinear oscillations increases.     

Acousto-optic interaction in laser vibrometry in a liquid

It is demonstrated that, when the classical method of laser vibrometry is used for measurements in a liquid, it gives erroneous results with measurement errors reaching 100% or more. The vibration pattern observed in this case exhibits a false structure with a spatial scale identical to the wavelength of acoustic waves in the liquid. In addition, the laser vibrometer shows displacements in the regions where they are actually absent. In the transient mode of operation, the image displays nonexistent surface waves, which propagate with the velocity of sound in the liquid. The origin of these distortions lies in the acoustooptic interaction that occurs in the condensed medium on the path of the probing laser beam. An analytic expression is obtained for the Green’s function characterizing laser vibrometry in the cases of harmonic and pulsed excitation of the surface under investigation. It is shown that this function explains all the artifacts observed in laser vibrometry in a liquid and can be used to correct the measurement data.     

离子液体Ammoeng 100与水之间相互作用的红外光谱分析

本文研究测量了Ammoeng 100与其水溶液在不同压力环境下的红外光谱,以期了解该离子液体与水之间的相互作用.结果表明,Ammoeng 100与水之间的相互作用主要来自离子液体的阴离子与水分子,且两者会根据能量稳定性而有选择性的接近;相对于阴离子,Ammoeng 100的烷基链受D_2O的扰动不大.与纯Ammoeng 100相比,在Ammoeng 100/D_2O的红外光谱中显示烷基C-H伸缩振动频率并没有太大变化,而压力小于1.0 GPa时D_2O会造成在Ammoeng 100的S=O对称伸缩振动频率红移.压力大于1.0GPa时,纯Ammoeng 100与Ammoeng 100/D_2O中的S=O对称伸缩振动频率大同小异,表明高压环境下D_2O不会对阴离子的对称伸缩振动频率造成明显影响,同时也显示离子液体在极性区的缔合结构会受到高压的扰动而有显著变化.