双模态振幅调制原子力显微术相互作用区转变研究

双模态振幅调制原子力显微术测试或成像过程中存在引力区和斥力区两种相互作用区.开展双模态振幅调制原子力显微术针尖样品相互作用区转变的研究,对于在特定作用区内成像的参数设置、相互作用区范围的控制,以及对成像结果的正确理解和解释尤为重要.将有限差分法和同相正交法相结合,采用数值模拟方法研究了探针模态自由振幅大小设定、样品力学性能变化以及模态激励频率的设置对双模态振幅调制原子力显微术相互作用区转变的影响.研究结果表明,探针模态自由振幅之和越大,则引力区向斥力区转变时的临界设定点越大,使探针位于引力区的设定点的范围越小.样品的弹性模量越大、黏度系数越小,探针在接近样品过程中引力区向斥力区转变发生越早,即引力区设定点的范围越小.偏离自由共振频率对探针进行激励时,引力区的范围均小于以自由共振频率激励时的引力区范围,探针运动状态的突变并不一定对应相互作用区的转变,且不能将相位值是否高于或低于90°作为判定探针位于引力区或斥力区的依据.     

双模态振幅调制原子力显微术对比度反转研究

双模态振幅调制原子力显微术广泛应用于微纳米力学成像,然而成像过程中可能存在的对比度反转问题会造成成像结果的难以理解和解释。将有限差分法和同相正交法相结合,采用数值方法研究了不同力常数探针、样品组分力学性能以及成像参数设置对双模态振幅调制原子力显微术二阶模态振幅和相位对比度反转的影响。研究结果显示,对于硬探针,不同粘度系数组分上二阶模态振幅和相位对比度随弹性模量增加无反转产生。探针在不同弹性模量组分上二阶模态振幅对比度随粘度系数增加会产生反转,而二阶模态相位对比度则无反转产生。对于软探针,组分弹性模量或粘度系数增加会造成相互作用区转变,使探针响应产生跳变。软探针在组分弹性模量较高时二阶模态相位对不同粘度系数的对比度以及在粘度系数较小时对不同弹性模量组分的对比度均较硬探针更低。两种探针在不同弹性模量组分上二阶模态振幅对比度随着二阶模态自由振幅的增加会发生反转,而不同粘度系数下的对比度则未出现反转。此外,二阶模态自由振幅越小,则二阶模态相位对不同弹性模量或粘度系数组分的对比度越高。二阶模态振幅或相位对比度在不同相互作用区可能会发生反转,成像时应使相互作用区处于排斥区,可提高对比度。     

双模态振幅调制原子力显微术对比度反转研究

双模态振幅调制原子力显微术广泛应用于微纳米力学成像,然而成像过程中可能存在的对比度反转问题会造成成像结果的难以理解和解释。将有限差分法和同相正交法相结合,采用数值方法研究了不同力常数探针、样品组分力学性能以及成像参数设置对双模态振幅调制原子力显微术二阶模态振幅和相位对比度反转的影响。研究结果显示,对于硬探针,不同粘度系数组分上二阶模态振幅和相位对比度随弹性模量增加无反转产生。探针在不同弹性模量组分上二阶模态振幅对比度随粘度系数增加会产生反转,而二阶模态相位对比度则无反转产生。对于软探针,组分弹性模量或粘度系数增加会造成相互作用区转变,使探针响应产生跳变。软探针在组分弹性模量较高时二阶模态相位对不同粘度系数的对比度以及在粘度系数较小时对不同弹性模量组分的对比度均较硬探针更低。两种探针在不同弹性模量组分上二阶模态振幅对比度随着二阶模态自由振幅的增加会发生反转,而不同粘度系数下的对比度则未出现反转。此外,二阶模态自由振幅越小,则二阶模态相位对不同弹性模量或粘度系数组分的对比度越高。二阶模态振幅或相位对比度在不同相互作用区可能会发生反转,成像时应使相互作用区处于排斥区,可提高对比度。     

多模态原子力显微术研究进展

材料纳米尺度的各种性能中，纳米力学性能是纳米材料和器件服役所需要保证的最基本性能。因此，发展可靠的定量化纳米力学测试技术就显得尤为关键。原子力显微镜(Atomic Force Microscope，AFM)作为纳米力学测试的重要平台，目前广泛应用于材料纳米尺度形貌和力学性能成像。作为原子力显微术的前沿应用模式之一，多模态原子力显微术通过同时激励探针的两个或多个振动模态对样品进行测试或成像，可实现对被测样品高分辨率、高灵敏度、定量化和无损的纳米力学快速成像及检测，具有极其广泛的应用前景。围绕多模态原子力显微术，首先介绍了多模态原子力显微术的基本成像原理和力学模型基础。随后，综述了多模态原子力显微术探针动力学以及成像技术相关研究的主要进展。然后，对多模态原子力显微术的几类典型应用进行了总结和评述。最后，对多模态原子力显微术未来可能的研究方向进行了展望。     

双模态发动机的模态鉴别方法

双模态冲压发动机的不同燃烧模态具有不同的稳焰机制和流态特征,并且在模态转换时伴随着显著的推力变化. 因此,准确判断燃烧模态,对于捕捉发动机的燃烧区位置/范围、释热分布特征,以及为进一步优化燃烧室的设计(流道结构和供油布局) 具有重要意义. 目前尚无鉴别模态的有效试验方法,本文提出了一种模态鉴别的试验方法,并在超燃直连台上开展验证试验. 试验中使用的测量技术包括:壁面静压、高速阴影/纹影、多通道可调谐二极管吸收光谱和高能态碳氢自由基CH* 自发光成像. 利用多种测量方法的组合,可以同时获得燃烧室中气流静温、速度、马赫数分布,释热分布以及燃烧区位置/范围. 这些试验数据能够用于判别模态,并获得不同模态的流动和火焰特征.      

流向振荡圆柱绕流的格子Boltzmann方法模拟

用一种新近发展起来的格子Boltzmann方法(LBM)在相对较小的雷诺数(Re \le 200)条件下模拟了不可压缩的流向振荡圆柱绕流问题, 考查了涡脱落模态和升阻力特性. 通过模拟, 在近尾流区发现了实验研究中已经发现的对称/反对称的涡脱落模态, 包括有些传统数值方法未发现的模态. 研究了频率锁定区域的范围及其与振幅的关系, 发现振幅越大, 发生锁定的频率区域越宽. 此外还对升阻力进行了定量意义的模拟,研究了振荡频率和振幅与升阻力的关系.      

有限厚度模型校准二维MoS2的Bimodal-AFM杨氏模量测量

二维材料因其独特的晶体结构、新奇的物理特性和优异的力学性能, 在微纳机电系统、柔性电子器件等诸多领域有着广阔的应用前景. 弹性模量是二维材料的基本力学特性参量之一, 对其器件应用及应变调控有重要影响. 受限于二维结构和原子级厚度特征, 难以实现二维材料弹性模量的精确测量. 双模原子力显微镜的振幅调制-频率调制模式是一种高效测量二维材料杨氏模量的方法, 但刚性衬底对测量结果的影响不可忽视. 本工作通过双模原子力显微镜直接测得衬底与二维硫化钼的杨氏模量分布图, 并基于有限厚度模型对衬底效应进行修正, 得到了样品的本征杨氏模量值. 利用第一性原理计算得到了二维二硫化钼的弹性系数和杨氏模量, 对比发现实验和计算结果相当. 这说明双模原子力显微镜测量是一种可靠的二维材料杨氏模量直接测试方法, 且该方法无需制备悬空二维材料等繁琐步骤, 避免了常规测试中的不足. 本工作为大面积二维材料薄膜力学性能的程序化测试分析以及高通量力学实验数据的统计分析提供了可靠的实验基础.      

ENERGY DISSIPATION IN TAPPING MODE ATOMIC FORCE MICROSCOPY

原子力显微镜有多种成像模式,其中轻敲模式是最为常用的扫描方式.轻敲模式能获取样品表面形貌的高度信息和相位信息,其中相位信息具有更多的价值,如能反映样品的表面能、弹性、亲疏水性等.依据振动力学理论,相位与振动系统的能量耗散有关.探针样品间的能量耗散对于理解轻敲模式下原子力显微镜的成像机理至关重要,样品特性和测量环境会影响能量耗散.本文在不考虑毛细力影响下,基于JKR接触模型,给出了探针样品相互作用下的加卸载曲线,结合原子力显微镜力曲线实验,给出了探针-样品分离失稳点的位置,从而计算一个完整接触分离过程的能量耗散,进而讨论考虑表面粗糙度对能量耗散的影响.在轻敲模式下考虑毛细力影响,通过特征时间对比,证明挤出效应是液桥生成的主导因素,在等容条件下,用数值方法计算了不同相对湿度对能量耗散的影响.通过一维振子模型,简要说明原子力显微镜相位像与样品表面能、杨氏模量、表面粗糙度、相对湿度之间的关系.分析表明,表面粗糙度和环境湿度均会引起相位的变化,进而认为它们是引起赝像的因素.     

轻敲模式下原子力显微镜的能量耗散

原子力显微镜有多种成像模式,其中轻敲模式是最为常用的扫描方式.轻敲模式能获取样品表面形貌的高度信息和相位信息,其中相位信息具有更多的价值,如能反映样品的表面能、弹性、亲疏水性等.依据振动力学理论,相位与振动系统的能量耗散有关.探针样品间的能量耗散对于理解轻敲模式下原子力显微镜的成像机理至关重要,样品特性和测量环境会影响能量耗散.本文在不考虑毛细力影响下,基于JKR接触模型,给出了探针样品相互作用下的加卸载曲线,结合原子力显微镜力曲线实验,给出了探针-样品分离失稳点的位置,从而计算一个完整接触分离过程的能量耗散,进而讨论考虑表面粗糙度对能量耗散的影响.在轻敲模式下考虑毛细力影响,通过特征时间对比,证明挤出效应是液桥生成的主导因素,在等容条件下,用数值方法计算了不同相对湿度对能量耗散的影响.通过一维振子模型,简要说明原子力显微镜相位像与样品表面能、杨氏模量、表面粗糙度、相对湿度之间的关系.分析表明,表面粗糙度和环境湿度均会引起相位的变化,进而认为它们是引起赝像的因素.     

原子力显微镜探针振动的简化模型分析

为对原子力显微镜(atomic force microscope,AFM)的微悬臂梁进行定性动力学特性分析,建立AFM微悬臂梁的简化模型,探讨AFM探针的受迫振动.通过理论计算得出AFM探针简化模型的运动方程,并得到振动波形,证明了AFM实际应用中的对称问题和"频漂"问题,并发现AFM简化模型的间歇式碰撞现象.用负弹簧模拟探针针尖与样品之间的长程引力,并通过理论计算探讨长程引力对AFM测量的影响.     

Theory of amplitude modulation atomic force microscopy with and without Q-Control

The present text reviews the fundamentals of amplitude-modulation atomic force microscopy (AM-AFM), which is frequently also referred to as dynamic force microscopy, non-contact atomic force microscopy, or “tapping mode” AFM. It is intended to address two different kinds of readerships. First, due to a thorough coverage of the theory necessary to explain the basic features observed in AM-AFM, it serves theoreticians that would like to gain overview on how nanoscale cantilevers interacting with the surrounding environment can be used to characterize nanoscale features and properties of suitable sample surfaces. On the other hand, it is designed to introduce experimentalists to the physics underlying AM-AFM measurements to a degree that is not too specialized, but sufficient to allow them measuring the quantities they need with optimized imaging parameters.More specifically, this article first covers the basics of the various driving mechanisms that are used in AFM imaging modes relying on oscillating cantilevers. From this starting point, an analytical theory of AM-AFM is developed, which also includes the effects of external resonance enhancement (“Q-Control”). This theory is then applied in conjunction with numerical simulations to various situations occurring while imaging in air or liquids. In particular, benefits and drawbacks of driving exactly at resonance frequency are examined as opposed to detuned driving. Finally, a new method for the continuous measurement of the tip-sample interaction force is discussed.     

Two-phase slug flows in helical pipes: Slug frequency alterations and helicity fluctuations

Air-water numerical simulations in the slug flow regime have been performed in horizontal helical pipes and the effects of geometries on the flow regime have been investigated. Depending on the length of the helix, outlet slug frequencies have been reduced with various degrees of efficiency. Correlations between mean tangential velocity and helicity density fluctuations have been identified and investigated qualitatively. These flow fields show smaller time scales than those obtained in volume fractions fluctuations. Shifts observed in the tangential velocity and mean helicity fluctuations to smaller time scales (high frequencies) are associated with regime transitions. For a slug flow undergoing a continuous transition to the annular flow regime, it is shown that the presence of slower (low frequencies) helicity fluctuations is attributed to the variations in the axial velocity. Finally, the analysis of the helicity at gas-liquid interface confirms the presence of the mixing zone at the slug front.     

Parametric random excitation of nonlinear coupled oscillators

The stochastic bifurcation and response statistics of nonlinear modal interaction under parametric random excitation are studied analytically, numerically and experimentally. Two basic definitions of stochastic bifurcation are first introduced. These are bifurcation in distribution and bifurcation in moments. bifurcation in moments is examined for the case of a coupled oscillator subjected to parametric filtered white noise. The center frequency of the excitation is selected to be close to either twice the first mode or second mode natural frequencies or the sum of the two. The stochastic bifurcation in moments is predicted using the Fokker-Planck equation together with gaussian and non-Gaussian closures and numerically using the Monte Carlo simulation. When one mode is parametrically excited it transfers energy to the other mode due to nonlinear modal interaction. The Gaussian closure solution gives close results to those predicted numerically only in regions well remote from bifurcation points. However, bifurcation points predicted by the non-Gaussian closure are in good agreement with those estimated by numerical simulation. Depending on the excitation level, the probability density of the excited mode is strongly non-Gaussian and exhibits multi-maxima as predicted by Monte Carlo simulation. Experimental tests are carried out at relatively low excitation levels. In the neighborhood of stochastic bifurcation in mean square the measured results exhibit different regimes of response characteristics including zero motion and occasional small random motion regimes. These two regimes are characterized by the phenomenon of on-off intermittency. Both regimes overlap and thus it is difficult to locate experimentally the bifurcation point.     

Empirical equations to predict flow patterns in two-phase inclined flow

Based on experimental data, flow regime maps were drawn for different inclination angles, including horizontal and vertical flow. Different empirical equations for the flow regime transitions are proposed that are functions of inclination angle for both upflow and downflow. In general, the flow regimes and their transitions for upflow were similar to those proposed by Duns and Ros for vertical upflow. For downflow, the flow regimes and their transitions conformed more to the Mandhane et al. type of flow regime map. The stratified flow region in downflow was found to be affected appreciably by the angle of inclination. A detailed comparison of the proposed transition equations with a number of flow regime maps is also presented.     

损伤效应对悬索2:1内共振响应影响分析

损伤是结构振动测试和运营维护中不可避免的问题，损伤效应会导致结构振动特性发生改变．本文以受损悬索为例，探究该非线性系统同时发生主共振和2:1内共振时，损伤效应对其面内耦合共振响应影响．首先基于哈密顿变分原理，引入与损伤程度、范围和位置相关的三个无量纲参数，建立受损悬索面内动力学模型，并推导其无穷维非线性运动微分方程．以2:1耦合共振为例，采用Galerkin法和多尺度法得到系统直角坐标形式的调谐方程．数值算例表明：损伤会导致悬索固有频率降低，使得频率间公倍关系发生改变，影响系统耦合共振响应；损伤会引发系统振动特性发生明显定量和定性改变，尤其是共振响应幅值及弹簧特性；损伤对直接激励模态响应幅值的影响比对内共振激发对响应幅值的影响要明显；损伤会导致霍普夫、鞍节点、叉形和倍周期分岔的位置发生偏移，从而影响分岔点附近系统的动力学行为；系统动态解和周期运动与损伤密切相关，损伤会导致系统展现出完全不同类型的吸引子．     

Three-to-one internal resonance in multiple stepped beam systems

In this study, the vibrations of multiple stepped beams with cubic nonlinearities are considered. A three-to-one internal resonance case is investigated for the system. A general approximate solution to the problem is found using the method of multiple scales （a perturbation technique）. The modulation equations of the amplitudes and the phases are derived for two modes. These equations are utilized to determine steady state solutions and their stabilities. It is assumed that the external forcing frequency is close to the lower frequency. For the numeric part of the study, the three-to-one ratio in natural frequencies is investigated. These values are observed to be between the first and second natural frequencies in the cases of the clamped-clamped and clamped-pinned supports, and between the second and third natural frequencies in the case of the pinned-pinned support. Finally, a numeric algorithm is used to solve the three-to-one internal resonance. The first mode is externally excited for the clamped-clamped and clamped-pinned supports, and the second mode is externally excited for the pinned-pinned support. Then, the amplitudes of the first and second modes are investigated when the first mode is externally excited. The amplitudes of the second and third modes are investigated when the second mode is externally excited. The force-response, damping-response, and .frequency- response curves are plotted for the internal resonance modes of vibrations. The stability analysis is carried out for these plots.     

Vortex-induced vibration of two elastically coupled cylinders in side-by-side arrangement

Vortex-induced vibration (VIV) of two elastically coupled circular cylinders in side-by-side arrangement is investigated numerically. The Reynolds-averaged Navier–Stokes equations are solved by the finite element method for simulating the flow and the equation of motion is solved for calculating the vibration. The mass ratio (the ratio of the mass of the cylinder to the displaced fluid mass) is 2 and the Reynolds number is 5000 in the simulations. Simulations are carried out for one symmetric configuration (referred to be Case A) and one asymmetric configuration (referred to be Case B). In both Case A and Case B, the primary response frequencies of the two cylinders are found to be the same both inside and outside the lock-in regimes. Five response regimes are found in both cases and they are the first-mode lock-in regime, the second-mode lock-in regime, the sum-frequency lock-in regime and two transition regimes. When the vibration is transiting from the first- to the second-mode lock-in regimes, the vibration of each cylinder contains both first- and the second-mode natural frequencies, and the vibrations are usually irregular. In the transition regime between the second-mode lock-in and the sum-frequency lock-in regimes, the response frequencies of both cylinders increases with an increase in the reduced velocity until they are close to the sum of the two natural frequencies. In both cases, the lower boundary reduced velocity of the total lock-in regime (the sum of the five lock-in regimes) is about 3 and the upper boundary reduced velocity is about 11 times the first-to-second-mode natural frequency ratio.     

On the development of an objective flow regime indicator

A high intensity dual beam X-ray system was designed and constructed to make chordal-average void fraction measurements. This X-ray system employed a DC excited tube filament, full wave rectification and high voltage filtering to produce a stable photon source. The large photon flux produced by the X-ray system allowed analog linearization of the signal.A series of chordal-average void fraction measurements were made and used to generate probability density functions (PDF) and power spectral density (PSD) functions. The first four moments associated with these distributions were studied as possible flow regime indicators.The moments of the PDF indicated the various flow regime transitions. The moments of the PSD also show some flow regime transition information, but were sensitive to liquid phase velocity. The PDF variance, or second moment about the mean, was found to be the best indicator of flow regime. A variance of 0.04 appear to adequately discriminate between the bubbly, slug and annular flow regimes for low pressure air/water flow in a 2.54 cm I.D. vertical tube.     

Free surface deformation frequencies of an electromagnetically excited mercury layer

Local measurements of the free surface frequencies of a mercury cylindrical layer submitted to a low frequency vertical magnetic field have been performed using a new resistive probe. The results confirm the linear analysis which predicts two types of classical transitions (harmonic and subharmonic) and a specific electromagnetic transition occurring with a combination of frequencies.The authors would like to thank the referees for their helpful comments during the revision which helped to make clearer the aim of this paper.