STUDY ON A DYNAMICS MODEL OF TAPPING MODE AFM AND ENERGY DISSIPATION MECHANISM$^{\bf 1)}$

轻敲模式下探针从远离到间歇性接触样品表面,是一个连续的能量耗散过程.针对该连续过程的能量耗散机理研究仅零星存在于各个文献之中,对于连续过程中各个阶段的能量耗散机理也没有一个系统的解释和实验验证.本文提出了新的位移激励下原子力显微镜探针-样品系统简化模型并得到了一维振子系统等效阻尼的计算方法,并通过该方法计算了探针在远离样品表面时的空气黏性阻尼和靠近样品时的空气压膜阻尼,分析了探针从远离样品到间歇性接触样品表面这一过程中的环境耗散机理变化,得到了原子力显微镜系统理论品质因数与探针工作位置的关系曲线;在此基础上设计了轻敲模式下的微悬臂梁扫频实验,得到了系统实验品质因数与探针工作位置的关系曲线,进而验证了理论模型的准确性. 本文通过对轻敲模式下AFM环境耗散机理进行理论分析和实验验证,希望可以对轻敲模式下AFM动力学特性及其阻尼作用机理有更近一步的认识,同时对微纳米机电系统 (MEMS/NEMS) 能量耗散机理的研究提供理论参考和实验方法.     

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.     

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.     

关于轻敲式原子力显微镜动力学系统中能量耗散的研究

原子力显微镜是一种典型的微纳谐振器,其核心部件是一个对微弱力极敏感的微悬臂梁探针,当它在不同的环境工作时,存在着各种不同形式、不同性质的能量耗散,这些能量耗散与系统的相位图像有着密切的联系.在众多的耗散机制中,只有针尖与样品的黏附接触耗散才能真正反映样品的性质,其他耗散会降低黏附接触耗散在系统总耗散中的占比,使得图像中的有效信息被削弱.因而,明确其他耗散对系统品质因数的量级贡献是十分重要的,这有助于提高图像的品质.为了研究这些耗散,本文根据耗散机理产生的原因对不同的能量耗散进行了细致的分类,系统总结了各种能量耗散的类型.之后,通过理论、实验和仿真的方法探究了在不同环境下、不同位置处微悬臂梁探针的能量耗散,明确了不同耗散对系统品质因数的量级贡献.然后,对于不同流体环境下的能量耗散,对比了它们的作用机理及量级大小.最后,对于在大气环境下工作的原子力显微镜探针,研究了它在振动过程中从高于样品表面到下降并接触样品这一连续过程中不同阶段存在的能量耗散,分析表明,在这些能量耗散中对系统品质因数影响最大的是由空气引起的耗散,包括空气黏性阻尼,压膜阻尼及液桥耗散.     

THE DISSIPATION ENERGY IN TAPPING MODE OF ATOMIC FORCE MICROSCOPE DUE TO LIQUID BRIDGE

轻敲模式下的相位像反映的是探针样品间接触分离过程的能量耗散, 大气环境下的能量耗散主要由液桥引起. 因此为理解成像机理, 本文分析轻敲模式下液桥的形成和破碎的动力学过程, 得到此种模式下的耗散能.     

基于能量传递规律的海洋立管涡激振动抑制研究

涡激振动是造成海洋立管疲劳损伤的重要因素, 抑制振动能够保障结构安全, 延长使用寿命. 多数涡激振动抑制方法基于干扰流场的方式, 但在复杂环境条件下, 仅通过干扰流场对振动的抑制效果有限. 因此, 从结构层面考虑开展了海洋立管涡激振动抑制研究. 基于能量传递的理论, 阐述了立管涡激振动过程中的能量传递规律. 振动能量以行波形式由能量输入区传播至能量耗散区, 主要在能量耗散区被消耗. 通过局部增大能量耗散区的阻尼, 增加振动能量在传播过程中的消耗, 实现涡激振动抑制. 为了求解立管涡激振动响应, 构建了尾流振子预报模型, 并根据实验结果验证了理论模型的可靠性. 基于理论计算得到的能量系数, 判定立管涡激振动的能量输入区和能量耗散区. 通过对比立管增大阻尼前后的响应, 分析了涡激振动抑制效果. 研究结果表明: 在能量输入区增大阻尼对涡激振动的抑制效果并不显著; 在能量耗散区增大阻尼使能量衰减系数达到临界值之后, 能够显著降低立管上部和底部的涡激振动位移; 当能量衰减系数超过临界值后, 继续增大耗散区阻尼对涡激振动抑制效果的提升不明显.      

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.     

粗糙表面的黏着试验研究

在微机械电子系统中,表面粗糙峰的几何特征、尺寸以及形状等对表面黏着以及摩擦特性有重要作用.为了研究粗糙度对黏着力的影响,首先用KOH溶液腐蚀硅片,得到8个粗糙度不同的样品.使用原子力显微镜(AFM)来测量样品的黏着力.分别使用两种探针来模拟不同的接触几何,第一种探针针尖为一个2μm左右的平台,另一种探针为尖探针.试验分别在干燥的手套箱内以及在空气中进行.在样品表面随机选取15个测量点,每个点测量50次,然后根据计算值,确定平面的平均黏着力以及标准差.并与Robinovich模型的计算结果作比较.结果显示:当粗糙度较小的时候,随着粗糙度增大,黏着力下降很快,这与Robinovich模型变化趋势较吻合;当粗糙度较大时,随着粗糙度增大黏着力略有增加,但不是很明显,与Robinovich模型相差较大.     

PVC发泡板受力前后微观表面形貌变化规律的AFM实验研究

本文从微观角度对软质材料之一的PVC发泡板表面形貌与承受压载之间的关系进行实验研究.应用Veeco原子力显微镜(AFM),选取全新的1cm×1cm大小的PVC实验样品,轻轻地放置于AFM样品台上.先测试和记录一定范围内的没有压载作用时试件的微观表面形貌,然后依次测试和记录承受过一定数目压载情形下的表面形貌.其中,压载通过标准计量的砝码实现,重复多次实验,将实验数据进行统计分析.结果显示,经压载作用后,PVC的微观表面特性变化明显.随着压载荷的增加,样品微观表面的高度变化量、平均高度、粗糙度等明显增加,截面起伏度也越加明显.本实验结果对于PVC材料宏观承载应用及其微观结构变化机理等方面的研究将具有一定的参考意义.     

表面活性物质对液体晃动阻尼影响分析及计算

对表面活性物质对液体晃动阻尼 的影响进行了理论分析, 针对液体小幅自由晃动对表面活性物质耗散阻尼计算公式进行了推 导. 在此基础上提出了结合液体晃动有限元计算的表面活性物质耗散阻尼的数值计算方法. 通过将算例结果与实验值和理论分析结果进行比较, 数值方法的有效性得到了验证.     

基于等效阻尼理论的金属橡胶弹性迟滞力学模型及实验研究

针对弹性多孔金属橡胶非线性迟滞特性力学行为,将迟滞恢复力-位移曲线分解为非线性单值曲线和椭圆,并将等效阻尼理论用于动态力学性能参数识别,从而建立了一种新型的适用于黏弹性阻尼材料的宏观唯象力学模型。采用不同相对密度的环形金属橡胶进行动态实验测试,以验证理论模型的准确性,结果表明该模型可将具有非线性特性的金属橡胶系统进行降阶处理,提高金属橡胶力学模型的预测效率,并能很好地描述金属橡胶的迟滞力学行为。另外,研究了在不同激励频率条件下金属橡胶的阻尼耗能特性。实验结果表明:在高频加载的条件下,黏性阻尼系数对动态加载频率不敏感,阻尼耗能与加载幅值之间呈线性正相关。基于等效阻尼理论的弹性迟滞力学模型具有一定的普适性,可进一步推广应用于类似弹性多孔材料的力学性能表征,为其工程应用提供理论基础。     

Modal interactions in contact-mode atomic force microscopes

Atomic force microscopes (AFM) are used to estimate material and surface properties. When using contact-mode AFM, the sample or the probe is excited near a natural frequency of the system to estimate the linear coefficient of the contact stiffness. Because higher modes offer lower thermal noise, higher quality factors, and higher sensitivity to stiff samples, their use in this procedure is more desirable. However, these modes are candidates for internal resonances, where the energy being fed into one mode may be channeled to another mode. Ignoring such interactions could distort or affect the accuracy of measurements. The method of multiple scales is used to derive an approximate analytical expression to the probe response in the presence of two-to-one autoparametric resonance between the second and third modes. We examine characteristics of this solution in relation to a single-mode response and consider its implications in AFM measurements. We find that the influence of this interaction extends over a considerable range of the tip-sample contact stiffness.     

Noise influenced elastic cantilever dynamics with nonlinear tip interaction forces

In this work, the authors study the influence of noise on the dynamics of base-excited elastic cantilever structures at the macroscale and microscale by using experimental, numerical, and analytical means. The macroscale system is a base excited cantilever structure whose tip experiences nonlinear interaction forces. These interaction forces are constructed to be similar in form to tip interaction forces in tapping mode atomic force microscopy (AFM). The macroscale system is used to study nonlinear phenomena and apply the associated findings to the chosen AFM application. In the macroscale experiments, the tip of the cantilever structure experiences long-range attractive and short-range repulsive forces. There is a small magnet attached to the tip, and this magnet is attracted by another one mounted to a high-resolution translatory stage. The magnet fixed to the stage is covered by a compliant material that is periodically impacted by the cantilever’s tip. Building on their earlier work, wherein the authors showed that period-doubling bifurcations associated with near-grazing impacts occur during off-resonance base excitations of macroscale and microscale cantilevers, in the present work, the authors focus on studying the influence of Gaussian white noise when it is included as an addition to a deterministic base excitation input. The repulsive forces are modeled as Derjaguin–Muller–Toporov (DMT) contact forces in both the macroscale and microscale systems, and the attractive forces are modeled as van der Waals attractive forces in the microscale system and magnetic attractive forces in the macroscale system. A reduced-order model, based on a single mode approximation is used to numerically study the response for a combined deterministic and random base excitation. It is experimentally and numerically found that the addition of white Gaussian noise to a harmonic base excitation facilitates contact between the tip and the sample, when there was previously no contact with only the harmonic input, and results in a response that is nominally close to a period-doubled orbit. The qualitative change observed with the addition of noise is associated with near-grazing impacts between the tip and the sample. The numerical and experimental results further motivate the formulation of a general analytical framework, in which the Fokker–Planck equation is derived for the cantilever-impactor system. After making a set of approximations, the moment evolution equations are derived from the Fokker–Planck equation and numerically solved. The resulting findings support the experimental results and demonstrate that noise can be added to the input to facilitate contact between the cantilever’s tip and the surface, when there was previously no contact with only a harmonic input. The effects of Gaussian white noise are numerically studied for a tapping mode AFM application, and it is shown that contact between the tip and the sample can be realized by adding noise of an appropriate level to a harmonic excitation.     

A new type of atomic force microscope based on chaotic motions

Local flow variation (LFV) method of non-linear time series analysis is applied to develop a chaotic motion-based atomic force microscope (AFM). The method is validated by analyzing time series from a simple numerical model of a tapping mode AFM. For both calibration and measurement procedures the simulated motions of the AFM are nominally chaotic. However, the distance between a tip of the AFM and a sample surface is still measured accurately. The LFV approach is independent of any particular model of the system and is expected to be applicable to other micro-electro-mechanical system sensors where chaotic motions are observed or can be introduced.     

An Internal Damping Model for the Absolute Nodal Coordinate Formulation

Introducing internal damping in multibody system simulations is important as real-life systems usually exhibit this type of energy dissipation mechanism. When using an inertial coordinate method such as the absolute nodal coordinate formulation, damping forces must be carefully formulated in order not to damp rigid body motion, as both this and deformation are described by the same set of absolute nodal coordinates. This paper presents an internal damping model based on linear viscoelasticity for the absolute nodal coordinate formulation. A practical procedure for estimating the parameters that govern the dissipation of energy is proposed. The absence of energy dissipation under rigid body motion is demonstrated both analytically and numerically. Geometric nonlinearity is accounted for as deformations and deformation rates are evaluated by using the Green–Lagrange strain–displacement relationship. In addition, the resulting damping forces are functions of some constant matrices that can be calculated in advance, thereby avoiding the integration over the element volume each time the damping force vector is evaluated.     

基于离散单元法的颗粒阻尼耗能减振特性研究

采用离散单元法并从能量耗散的角度研究颗粒阻尼对系统减振特性的影响。建立了颗粒介质细观下的法向、切向和滚动方向的粘弹性接触模型和能量耗散模型,通过冲击激励和简谐激励下系统振动响应的多参数能量耗散分析来研究颗粒阻尼的耗能机理和减振特性。数值试验表明,颗粒介质可以在一个较宽的振动幅值范围内有效的发挥其阻尼效应,其耗能具有阶梯状周期性的特点。填充率是影响颗粒阻尼耗能减振效果的主要工程可控参数并对系统共振频率产生重大影响,当填充率接近极值时,系统出现无阻尼共振及共振频率超出无颗粒系统固有频率的现象。系统在最优填充率下共振时,颗粒与箱体保持恒定相位差的超振幅稳态运动。较小粒径的颗粒可以提高能量耗散率并使振动系统更快趋向静平衡状态,而恢复系数和摩擦系数则对法向和切向耗能的比值有较大影响。