Sensitivity analysis of scanning near-field optical microscope probe

In this paper, we study the dynamic modes of a scanning near-field optical microscope (SNOM) which uses an optical fiber probe; and the sensitivity of flexural and axial vibration modes for the probe were derived and the closed-form expressions were obtained. According to the analysis, as expected each mode has a different sensitivity and the first mode is the most sensitive mode of flexural and axial vibration for the SNOM probe. The sensitivities of both flexural and axial modes are greater for a material surface that is compliant with the cantilever probe. As the contact stiffness increases, the high-order vibration modes are more sensitive than the lower-order modes. Furthermore, the axial contact stiffness has a significant effect on the sensitivity of the SNOM probe, and this should be noted when designing new cantilever probes.     

Vibration of scanning near-field optical microscope probe with laser-induced thermal effect using Timoshenko beam theory

The Timoshenko beam theory, including the effects of rotary inertia and shear deformation, is used to analyze the resonant frequency of lateral vibration of scanning near-field optical microscope (SNOM) tapered probe with a laser-induced thermal effect. In the analysis, the thermal effect can be considered as an axial force and is dependent of temperature distribution of the probe. The Rayleigh–Ritz method is used to solve the vibration problem of the probe. According to the analysis, the frequencies of the first three vibration modes increase when the thermal effect is taken into account. The effects of shear deformation and rotary inertia on the frequency ratio of a Timoshenko beam to an Euler beam increase when the mode number increases and the contact stiffness decreases. In addition, the frequency of mode 1 increases with increasing taper angle and coating thickness of the probe. Comparison of the frequency of a SNOM probe coated with Al, Ag, or Au, the highest is with Al coating, and the lowest is with Au coating.     

Sensitivity investigation of the different direction vibrations of a SNOM probe

In this article, we analyze the sensitivity of lateral, axial, and torsional vibration of a scanning near-field optical microscope (SNOM) probe. An exact solution for the title problem is obtained using the theory of beam and torsional vibrations. Sensitivities are obtained for a wide range of the intervening physical parameters. This paper discusses the relationship between the sensitivity of a SNOM probe and its geometry. The analysis is presented for a probe in three different cases lateral vibration, axial vibration, and torsional vibration, for a fixed-free configuration. To derive the mathematical relation between the probe and sample (by utilizing springs and damping to simulate different environments) through the process of theory analysis for different environments. Thus a universal touchless SNOM probe sensitivity controller is developed for appropriate control and adjustment of the probe sensitivity suitable under different environments. Such controller helps the SNOM probe achieve the nanoscale resolution through proper control and adjustment probe sensitivity in accordance to changes to different environments and reduce the chance of being damaged during the scan, which in the end further advances the sample inspection technique.     

SFM/SNOM结合的扫描探测显微镜

采用光纤探针的扫描近场光学显微镜 (SNOM)存在某些弱点 ,如探针特别脆 ,不易贴近样品表面扫描 ,探针的转输效率低等。近年来发展了将SFM /SNOM结合起来的扫描探测显微镜。利用微加工工艺技术 ,将小孔集成在悬臂探针中 ,使探针既能批量制备 ,又具有很好的重复性。探针悬臂在垂直于样品表面方向上的弹性常数较小 ,针尖不易损坏。在接触模式中利用这种SFM /SNOM组合探针可将样品的形貌像、摩擦力和光学透射像等信息同时记录下来。对于综合研究样品表面的介观性质十分有利。     

照明模式SNOM中样品对近场光场分布的影响

在同时考虑样品的形貌及材料光学参量和入射光偏振模式的情况下,利用基于边界元方法编写的二维矢量电磁场计算程序,对工作在照明模式下的扫描近场光学显微镜（Scanning Near-field Optical Microscope,SNOM）的近场矢量电磁场分布进行了数值计算模拟研究.结果表明,在没有表面形貌特征时,探针的光能量透射率随样品材料的折射率和损耗角的增加而增大,而样品表面光斑尺寸受折射率和损耗角的影响很小;对有形貌特征的探针扫描像研究结果表明,SNOM的分辨率随着样品的折射率和损耗角的增加而提高;对SNOM不同的工作模式的扫描成像信号进行的计算结果表明,恒定间距扫描方式比恒定高度扫描方式对样品表面的细节有较强的分辨能力.     

A distributed-mass approach for dynamic analysis of Bernoulli-Euler plane frames

The exact dynamic analysis of plane frames should consider the effect of mass distribution in beam elements, which can be achieved by using the dynamic stiffness method. Solving for the natural frequencies and mode shapes from the dynamic stiffness matrix is a nonlinear eigenproblem. The Wittrick-Williams algorithm is a reliable tool to identify the natural frequencies. A deflated matrix method to determine the mode shapes is presented. The dynamic stiffness matrix may create some null modes in which the joints of beam elements have null deformation. Adding an interior node at the middle of beam elements can eliminate the null modes of flexural vibration, but does not eliminate the null modes of axial vibration. A force equilibrium approach to solve for the null modes of axial vibration is presented. Orthogonal conditions of vibration modes in the Bernoulli-Euler plane frames, which are required in solving the transient response, are theoretically derived. The decoupling process for the vibration modes of the same natural frequency is also presented.     

考虑弯曲和轴向振动模态的一维梁压电阻抗模型及试验研究

同时考虑一维梁结构的弯曲和轴向振动,对其压电阻抗模型进行建模分析和试验验证。在0.02～42 kHz频段内区分并标记了一维钢梁弯曲振动模态前18阶及轴向振动模态前3阶。结果表明:在0.02～7.5kHz频段内,数值计算和试验结果中谐振峰对应频率的相对误差较大:11.7%～16.5%,其原因可能是低频时振动能量较低且波的传播受结构阻尼、边界条件及环境噪音等因素影响较为明显;在7.5～42kHz范围内,两者谐振峰位置符合良好,相对误差较小:0.11%～2.31%,表明该模型在高频段具有较好的适用性;轴向振动模态对应频率大于弯曲振动模态。本研究为结构健康监测过程中检测频段的选取及损伤信息的提取提供参考。     

Theoretical model of ball joint squeak

The theoretical model for the ball joint squeak problem is proposed. The ball joint is modeled as a sphere attached to a rotating flexible beam and it is in contact with a semi-spherical rigid socket. The relative rotation and vibration between the ball and socket produces friction stresses causing the dynamic instability of the system. The squeak propensity of the ball joint system is numerically investigated through the eigenvalue sensitivity analysis at the sliding equilibrium. Stability analysis shows that the bending modes of the beam can produce the dynamic instability under the negative friction-velocity slope. It is also highlighted that the squeak propensity under the poor friction characteristics can be controlled by the system parameters such as the sliding speed, the contact stiffness, the radius of the ball, the axial load and the tilting angle.     

Three-dimensional nonlinear vibration of gear pairs

This work investigates the three-dimensional nonlinear vibration of gear pairs where the nonlinearity is due to portions of gear teeth contact lines losing contact (partial contact loss). The gear contact model tracks partial contact loss using a discretized stiffness network. The nonlinear dynamic response is obtained using the discretized stiffness network, but it is interpreted and discussed with reference to a lumped-parameter gear mesh model named the equivalent stiffness representation. It consists of a translational stiffness acting at a changing center of stiffness location (two parameters) and a twist stiffness. These four parameters, calculated from the dynamic response, change as the gears vibrate, and tracking their behavior as a post-processing tool illuminates the nonlinear gear response. There is a gear mesh twist mode where the twist stiffness is active in addition to the well-known mesh deflection mode where the translational stiffness is active. The twist mode is excited by periodic back and forth axial movement of the center of stiffness in helical gears. The same effect can occur in wide facewidth spur gears if tooth lead modifications or other factors such as shaft and bearing deflections disrupt symmetry about the axial centers of the mating teeth. Resonances of both modes are shown to be nonlinear due to partial and total contact loss. Comparing the numerical results with gear vibration experiments from the literature verifies the model and confirms partial contact loss nonlinearity in experiments.     

Pole assignment of friction-induced vibration for stabilisation through state-feedback control

Friction-induced self-excited linear vibration is often governed by a second-order matrix differential equation of motion with an asymmetric stiffness matrix. The asymmetric terms are product of friction coefficient and the normal stiffness at the contact interface. When the friction coefficient becomes high enough, the resultant vibration becomes unstable as frequencies of two conjugate pairs of complex eigenvalues (poles) coalesce (when viscous damping is low).This short paper presents a receptance-based inverse method for assigning complex poles to second-order asymmetric systems through (active) state-feedback control of a combination of active stiffness, active damping and active mass, which is capable of assigning negative real parts to stabilise an unstable system.     

FREE VIBRATIONS OF SELF-STRAINED ASSEMBLIES OF BEAMS

This paper examines the natural frequencies and modes of transverse vibration of two simple redundant systems comprising straight uniform Euler-Bernoulli beams in which there are internal self-balancing axial loads (e.g., loads due to non-uniform thermal strains). The simplest system consists of two parallel beams joined at their ends and the other is a 6-beam rectangular plane frame. Symmetric mode vibration normal to the plane of the frame is studied. Transcendental frequency equations are established for the different systems. Computed frequencies and modes are presented which show the effect of (1) varying the axial loads over a wide range, up to and beyond the values which cause individual members to buckle (2) pinning or fixing the beam joints (3) varying the relative flexural stiffness of the component beams. When the internal axial loads first cause any one of the component beams to buckle, the fundamental frequency of the whole system vanishes. The critical axial loads required for this are determined. A simple criterion has been identified to predict whether a small increase from zero in the axial compressive load in any one member causes the natural frequencies of the whole system to rise or fall. It is shown that this depends on the relative flexural stiffnesses and buckling loads of the different members. Computed modes of vibration show that when the axial modes reach their critical values, the buckled beam(s) distort with large amplitudes while the unbuckled beam(s) move either as rigid bodies or with bending which decays rapidly from the ends to a near-rigid-body movement over the central part of the beam. The modes of the systems with fixed joints change very little (if at all) with changing axial load, except when the load is close to the value which maximizes or minimizes the frequency. In a narrow range around this load the mode changes rapidly. The results provide an explanation for some computed results (as yet unpublished) for the flexural modes and frequencies of flat plates with non-uniform thermal stress distributions.     

用扫描近场光学显微镜技术研究金膜表面等离体子共振

表面等离体子波(SPW)可与入射光横磁波极化能量耦合并被共振激发,这种现象被称为表面等离体子共振现象(SPR)。主要利用扫描近场光学显微镜(SNOM)技术和表面等离体子共振现象技术相结合,来研究金膜表面等离体子共振。设计并建立了结构独特的新型Kretschmann型表面等离体子共振现象耦合装置,同时又设计了具有厚度梯度的表面等离体子的制备方法。在此基础上,测量了改变入射角条件下的表面等离体子共振曲线,测得该装置的等离体子共振角灵敏度为1°。并且对金膜表面进行表面等离体子共振条件下的扫描近场光学显微成像。实验结果表明,在共振时金膜表面的扫描成像比不共振时清晰,而且增加了很多细节。应用表面等离体子共振现象技术将可以明显提高扫描近场光学显微镜的信噪比、分辨力等性能。     

A method to determine dynamic loads on spur gear teeth and on bearings

A method is described which can be used to calculate dynamic gear tooth force and bearing forces. The model includes elastic bearings. The gear mesh stiffness and the path of contact are determined using the deformations of the gears and the bearings. This gives contact outside the plane-of-action and a time-varying working pressure angle. In a numerical example it is found that the only important vibration mode for the gear contact is the one where the gear tooth deformation is dominant. The bearing force variation, however, will be much more affected by the other vibration modes. The influence of the friction force is also studied. The friction has no dynamic influence on the gear contact force or on the bearing force in the gear mesh line-of-action direction. On the other hand, the changing of sliding directions in the pitch point is a source for critical oscillations of the bearings in the gear tooth frictional direction. These bearing force oscillations in the frictional direction appear unaffected by the dynamic response along the gear mesh line-of-action direction.     

扫描近场光学显微镜的光耦合偶极子模型

为了研究扫描近场光学显微镜中探针和粗糙样品表面的耦合相互作用,提出了一种光耦合偶极子模型.在该模型中,探针和样品突起都由光极化偶极子表示,在准静态电磁场近似的情况下样品表面的诱导极化效应由影像偶极子表示,应用偶极子辐射理论可以得到系统的自洽场方程.此模型提供了一种直观分析扫描近场光学显微镜中探针和样品相互作用机理的方法.在此基础上,进一步讨论了金属样品的近场成像特点和其特有的局域光学共振现象.数值结果表明：不同于一般的介质样品,金属样品的近场图像与入射光频率直接相关,改变入射光的频率,获得的样品近场图像的形状和对比度都会发生变化.特别是当入射光频率处于样品极化共振范围内时,金属纳米粒子的极化率会出现光极化共振,这样就可以获得样品粒子的最大有效尺寸,为提高系统的分辨率提供了一条重要途径.     

“禁戒光”近场光学显微镜原理与系统

扫描近场光学显微术是８０年代后期发展起来的一种分辨率超过衍射极限的新型光学显微镜技术。本文介绍了国外最近出现的“禁戒光”近场光学显微镜系统的工作原理及结构。透射式ＳＮＯＭ中部分光沿着光轴向前传播；部分光沿着大于全内反射临界角的方向传播。前者称为允许光；后者称为禁戒光。应用“禁戒光”近场光学显微镜可同时获得三幅图像，即允许光像、禁戒光像和反映样品表面形貌的剪切力图像。禁戒光图像能够提供很好的对比度和分辨率。     

Dynamic identification of beam axial loads using one flexural mode shape

In the last decades, various methods have been proposed for the experimental evaluation of tensile forces acting in tie-beams of arches and vaults. Moreover, static and dynamic approaches have been formulated to evaluate critical compressive axial forces and flexural stiffness of end constraints. Adopting Euler–Bernoulli beam model, this paper shows that, if bending stiffness and mass per unit length of a beam with constant cross-section are known, the axial force and the flexural stiffness of the end constraints can be deduced by one vibration frequency and three components of the corresponding mode shape. Finally, data conditions are given to assess a physically admissible identification of the unknown parameters.     

液晶染料填充阶梯型Double-period结构局域模的光学特性

利用传输矩阵法研究了液晶染料填充一维阶梯型Double-period第四代准周期结构局域模的光学特性。计算了增益前局域模与外加电场方向和正入射波方向间夹角θ的变化关系,分析了增益系数与局域模透射率的关系以及局域模在空间位置的光场分布,讨论了增益后的局域模透射率与光场强度的关系。结果表明:随着夹角θ的增大,光子禁带变宽并且只向短波方向拓展;随着夹角θ的增大,增益前的局域模向短波方向移动,透射率逐渐增大,且局域模波长的调控量为23.7nm。随着增益系数的增大,透射率先增大后减小。光场分布呈现局域现象,当夹角θ=43.4°,波长λ=595.0nm时,光强达到6个数量级。增益后的局域模透射率与光场强度呈正比关系。     

A distributed-mass approach for dynamic analysis of Timoshenko plane frames

The dynamic stiffness method is the exact method for the dynamic analysis of plane frames using the continuous-coordinate system to consider the effect of mass distribution in beam elements. The dynamic stiffness method may create some null modes where the joints of beam element have null deformation. Unlike the Bernoulli–Euler frames, adding an interior node at the middle of the beam elements cannot normalize all the null modes of flexural vibration in the Timoshenko frames. The floating interior-node scheme is proposed to eliminate the null modes of flexural vibration in the Timoshenko frames. Orthogonal properties of vibration modes in Timoshenko plane frames are theoretically derived, through which the equations of motion in beam elements can be transformed into the decoupled equations of motion in terms of mode amplitudes.     

Parametric response of viscoelastically supported beams

The stability of viscoelastic beams with an attached mass and viscoelastic end supports under axial and tangential periodic loads is investigated. Viscoelastic end supports are substituted for translational and rotational springs with viscoelastic damping. The regions of instability for simple and combination resonances are obtained from the ordinary Mathieu equation which is obtained from the equation of motion by application of Galerkin's method. In numerical computations, the influences of the direction of loading, the attached mass, the support stiffness, and the damping on the regions of instability for simple and combination resonances are clarified.     

Analysis of flexural wave velocity and vibration mode in thin cylindrical shell

The relationship between the flexural wave velocity and the excited vibration mode of a thin cylindrical shell is investigated. The natural frequency corresponding to the vibration mode is obtained as the solution of characteristic equation of thin cylindrical shell. However, all of these vibration modes are not excited actually. To estimate the excited vibration mode, the concept of "modified bending stiffness" is introduced, and the influence of each stress component upon the modified bending stiffness is analyzed. The excited mode is theoretically discriminated from the nonexcited mode based on the smallness of this modified bending stiffness. The validity of our theory is confirmed by an excellent agreement between theoretical and experimental results on flexural wave velocity.