Sub-Angstrom oscillation amplitude non-contact atomic force microscopy for lateral force gradient measurement

We report the first results from novel sub-Angstrom oscillation amplitude non-contact atomic force microscopy developed for lateral force gradient measurements. Quantitative lateral force gradients between a tungsten tip and Si(1 1 1)-(7 × 7) surface can be measured using this microscope. Simultaneous lateral force gradient and scanning tunnelling microscope images of single and multi atomic steps are obtained. In our measurement, tunnel current is used as feedback. The lateral stiffness contrast has been observed to be 2.5 N/m at single atomic step, in contrast to 13 N/m at multi atomic step on Si(1 1 1) surface. We also carried out a series of lateral stiffness-distance spectroscopy. We observed lateral stiffness-distance curves exhibit sharp increase in the stiffness as the sample is approached towards the surface. We usually observed positive stiffness and sometimes going into slightly negative region.     

Stability and performance limits for active vibration isolation using blended velocity feedback

This paper presents a theoretical study of active vibration isolation on a two degree of freedom system. The system consists of two lumped masses connected by a coupling spring. Both masses are also attached to a firm reference base by a mounting spring. The lower mass is excited by a point force. A reactive control force actuator is used between the two masses in parallel with the coupling spring. Both masses are equipped with an absolute velocity sensor. The two sensors and the actuator are used to implement velocity feedback control loops to actively isolate the upper mass from the vibrations of the lower mass over a broad range of frequencies. The primary concern of the study is to determine what type of velocity feedback configuration is suitable with respect to the five parameters that characterise the system (the three spring stiffnesses and the two masses). It is shown analytically that if the ratio of the lower mounting spring stiffness to the lower mass is larger than the ratio of the upper mounting spring stiffness to the upper mass (supercritical system), feeding back the absolute upper mass velocity to the reactive force actuator results in an unconditionally stable feedback loop and the vibration isolation objective can be fully achieved without an overshot at higher frequencies. In contrast, if the ratio of the lower mounting spring stiffness to the lower mass is smaller than the ratio of the upper mounting spring stiffness to the upper mass (subcritical system), the upper mass velocity feedback is conditionally stable and the vibration isolation objective cannot be accomplished in a broad frequency band. For subcritical systems a blended velocity feedback is proposed to stabilise the loop and to improve the broad-band vibration isolation effect. A simple inequality is introduced to derive the combinations between the two error velocities that guarantee unconditionally stable feedback loops.     

Sensor fusion for active vibration isolation in precision equipment

Sensor fusion is a promising control strategy to improve the performance of active vibration isolation systems that are used in precision equipment. Normally, those vibration isolation systems are only capable of realizing a low transmissibility. Additional objectives are to increase the damping ratio of internal vibration modes and to provide a high support stiffness. It is shown that these three objectives cannot be realized simultaneously if only acceleration or force feedback is used. An active hard mount suspension with a feedback strategy based on sensor fusion is proposed that uses the acceleration signal at low frequencies and the force signal at high frequencies. Using sensor fusion, the three objectives can be achieved simultaneously. Experiments on a single-axis setup show that this feedback strategy provides an excellent performance.     

The grounds for time dependent market potentials from dealers’ dynamics

We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers’ feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market’s potential force. When markets are dominated by dealers with positive feedback the resulting potential force is repulsive, while the effect of negative feedback enhances the attractive potential force.     

Novel active noise-reducing headset using earshell vibration control

Active noise-reducing (ANR) headsets are available commercially in applications varying from aviation communication to consumer audio. Current ANR systems use passive attenuation at high frequencies and loudspeaker-based active noise control at low frequencies to achieve broadband noise reduction. This paper presents a novel ANR headset in which the external noise transmitted to the user's ear via earshell vibration is reduced by controlling the vibration of the earshell using force actuators acting against an inertial mass or the earshell headband. Model-based theoretical analysis using velocity feedback control showed that current piezoelectric actuators provide sufficient force but require lower stiffness for improved low-frequency performance. Control simulations based on experimental data from a laboratory headset showed that good performance can potentially be achieved in practice by a robust feedback controller, while a single-frequency real-time control experiment verified that noise reduction can be achieved using earshell vibration control.     

Mechanochemical Coupling of Kinesin Studied with a Neck-Linker Swing Model

A neck-linker swing model has been proposed in this work to investigate the mechanochemical coupling of kinesin. The difference between force-velocity curves given by force clamp and fixed trap respectively has been satisfactorily interpreted by this model. The study implies that ADP releasing and ATP hydrolysis are much less forcedependent in force clamp experiments than that in fixed trap experiments in the regime of moderate loading force, which might be a consequence of the delayed response of servo system in force clamp experiments.     

Dynamic characteristics of launch vehicle and spacecraft connected by clamp band

Spacecraft is usually fastened to the launch vehicle by clamp band in the aerospace industry. The application of clamp band joint brings local stiffness variation to the launch vehicle and spacecraft (LV/SC) system and affects the dynamic characteristics of the system. In this paper, the dynamic responses of the LV/SC system to the vibration and impact excitations were studied, where the effect of the clamp band joint was taken into account. Firstly, the mathematical model of the axial stiffness of the clamp band joint was derived. In the model, contact and slippage between the components were accommodated. Then the stiffness model was employed to construct the coupling dynamic model for the LV/SC system using the finite element software ANSYS. Finally, modal analysis and response analysis were carried out on the coupling dynamic model to investigate the dynamic characteristics of the LV/SC system; the simulation results were compared with those based on the dynamic model where the launch vehicle and the spacecraft were considered to be fixed together to explore the effect of the clamp band joint on the LV/SC system.     

Passive-active vibration isolation systems to produce zero or infinite dynamic modulus: theoretical and conceptual design strategies

The application of mechanical springs connected in parallel and/or in series with active springs can produce dynamical systems characterised by infinite or zero value stiffness. This mathematical model is extended to more general cases by examining the dynamic modulus associated with damping, stiffness and mass effects. This produces a theoretical basis on which to design an isolation system with infinite or zero dynamic modulus, such that stiffness and damping may have infinite or zero values. Several theoretical designs using a mixture of passive and active systems connected in parallel and/or in series are proposed to overcome limitations of feedback gain experienced in practice to achieve an infinite or zero dynamic modulus. It is shown that such systems can be developed to reduce the weight supported by active actuators as demonstrated, for example, by examining suspension systems of very low natural frequency or with a very large supporting stiffness or with a viscous damper or a self-excited vibration oscillator. A more general system is created by combining these individual systems allowing adjustment of the supporting stiffness and damping using both displacement and velocity feedback controls. Frequency response curves show the effects of active feedback control on the dynamical behaviour of these systems. The theoretical design strategies presented can be applied to design feasible hybrid vibration control systems displaying increased control performance.     

Axial deviation of an optically trapped particle in trapping force calibration using the drag force method

The axial deviation of the trapped particle in the lateral trap stiffness calibration and the maximal trapping force measurement has been reported, but has not yet been extensively analyzed in the literature. Due to the importance of the trapping force calibration in the applications, the axial deviation and the influence on the trap stiffness and the maximal trapping force measurement is analyzed both experimentally and theoretically. First, the trap stiffness calibration experiment is rechecked and more attention is paid to the axial displacement of the particle. The result confirms that the equilibrium position of the particle moves upward with the increase of the lateral displacement. In order to get better understanding of the phenomenon, the relation between the axial displacement and the lateral displacement is theoretically calculated by using the ray optics model. The comparison of the calculated result with the experimental one indicates that the particle equilibriums are not in the horizontal plane passing through the trap center, but are on a curved track where the external force is balanced with the trapping force. Then the relations between the trapping efficiency and the lateral displacement are derived, which shows that the experimentally calibrated trap stiffness is a reasonable approximation so long as the particle is kept in the central part of the trap. Finally, the difference between the maximal lateral trapping force and the escape force is discussed, and it is shown that the measured escape force is not as supposed to be the maximal lateral trapping force but far less than it.     

Determination of the axial force on stay cables accounting for their bending stiffness and rotational end restraints by free vibration tests

Determination of the axial force in terms of its natural frequencies may be significantly influenced by the bending stiffness of the cable and the rotational elastic restraints at the ends, depending on the geometrical and mechanical parameters of the cable and its supports and restraints, particularly in cement-grouted parallel-bundle wire cables. The paper presents an explicit analytical expression for the natural frequencies taking into account both the bending stiffness of the cable and the rotational restraint at the ends that may be used to determine the axial force. While the bending stiffness of the cable and the axial force are selected as variables to attain an optimal match between analytical and experimental data, the rotational stiffness at the ends is treated as a known parameter in that process. The degree of rotational restraint at the ends cannot be accurately inferred from the sequence of the experimentally determined natural frequencies, since this parameter does not appreciably affect the progression of their values. Techniques are discussed that allow approximate determination of the rotational stiffness at the ends for the most common arrangements of anchors and cables with, and without, intermediate supports provided by deviators located near the ends. The axial force and the bending stiffness of the cable are both simultaneously adjusted by matching the natural frequencies of the analytical model with the experimental values. The proposed approach leads to a reduction of the error in the estimation of the axial force for short cables with relatively high bending stiffness such as those typical of cement-grouted parallel-bundle wire cables often used as cable stays for bridges until the early 1990s.     

Theoretical comparison of optical traps created by standing wave and single beam

We used generalised Lorenz–Mie scattering theory (GLMT) to compare submicron-sized particle optical trapping in a single focused beam and a standing wave. We focus especially on the study of maximal axial trapping force, minimal laser power necessary for confinement, axial trap position, and axial trap stiffness in dependency on trapped sphere radius, refractive index, and Gaussian beam waist size. In the single beam trap (SBT), the range of refractive indices which enable stable trapping depends strongly on the beam waist size (it grows with decreasing waist). On the contrary to the SBT, there are certain sphere sizes (non-trapping radii) that disable sphere confinement in standing wave trap (SWT) for arbitrary value of refractive index. For other sphere radii we show that the SWT enables confinement of high refractive index particle in wider laser beams and provides axial trap stiffness and maximal axial trapping force at least by two orders and one order bigger than in SBT, respectively.     

Force distortion in resonance testing of structures with electro-dynamic vibration exciters

Harmonic input force distortion which arises when systems are excited with electrodynamic exciters is shown to be predominantly second harmonic, the major source of the harmonic distortion being due to the vibration exciter characteristics. These are examined by experimentally determining the magnetic field strength properties of a typical exciter and the results show these to be a non-linear even function. This information is used with the equations of motion of the excited which are simulated on an analog computer. The computed force characteristics are shown to compare very closely with experimental results. The amount of second harmonic force distortion generated at a system resonance is analyzed by considering a simple single degree-of-freedom model. It is shown that the amount of force distortion is related to the damping of the system under test and the ratio of the exciter stiffness to the system stiffness. It is also shown that the force input to a system near a system resonance can vary considerably, even though the input current to the exciter is constant. These effects are shown to be due to the forces arising from the mass and stiffness characteristics of the exciter being used. Experimental tests on a simple system confirm the theoretical predictions.     

Lateral force microscopy in low normal force limit

We have studied frictional force between SiN tip and Si surface by using lateral force microscopy. The cantilever we have used has very low stiffness of 0.006 N/m, and the normal force acting on the surface was much lower than the attractive force such as van der Waals force. In this low normal force limit, it was found that the frictional force did not depend on the normal force. We suggest a calibration method to estimate the attractive force from the lateral force data in this limit. The estimated attractive force between Si sample and SiN tip with radius of 10 nm was 0.4 nN in flat region and 0.65 nN at the corner of a rectangular hole.     

Stability analysis of a rotor–bearing system with time-varying bearing stiffness due to finite number of balls and unbalanced force

Previous investigations have indicated that the finite number of balls can cause the bearing stiffness to vary periodically. However, effects of unbalanced force in a rotor–bearing system on the bearing stiffness have not received sufficient attention. The present work reveals that the unbalanced force can also make the bearing stiffness vary periodically. The parametric excitations from the time-varying bearing stiffness can cause instability and severe vibration under certain operating conditions. Therefore, the determination of the operating conditions of parametric instability is crucial to the design of high speed rotating machinery. In this paper, an extended Jones–Harris stiffness model is presented to ascertain the stiffness of the angular contact ball bearing considering five degrees of freedom. Stability analysis of a rigid rotor–bearing system is performed utilizing the discrete state transition matrix (DSTM) method. The effects of unbalanced force, bearing loads and damping on the instability regions are discussed thoroughly. Investigations mainly show that the time-varying bearing stiffness fluctuates sinusoidally due to finite number of balls and unbalanced force. The locations and widths of the instability regions caused by these two parametric excitations differ distinctly. Unbalanced force could change the widths of the instability regions, but without altering their central positions. The axial and radial loads of the bearing only change the positions of the instability regions, without affecting their widths. Besides, damping can reduce the widths of the instability regions.     

Force distributions and force chains in random stiff fiber networks

We study the elasticity of random stiff fiber networks. The elastic response of the fibers is characterized by a central force stretching stiffness as well as a bending stiffness that acts transverse to the fiber contour. Previous studies have shown that this model displays an anomalous elastic regime where the stretching mode is fully frozen out and the elastic energy is completely dominated by the bending mode. We demonstrate by simulations and scaling arguments that, in contrast to the bending dominated elastic energy, the equally important elastic forces are to a large extent stretching dominated. By characterizing these forces on microscopic, mesoscopic and macroscopic scales we find two mechanisms of how forces are transmitted in the network. While forces smaller than a threshold F_c are effectively balanced by a homogeneous background medium, forces larger than F_c are found to be heterogeneously distributed throughout the sample, giving rise to highly localized force chains known from granular media.     

Controlling chaos: Stabilization of unstable orbits using exponential control for maps and flows

We demonstrate that chaos can be controlled using multiplicative exponential feedback control. Unstable fixed points, unstable limit cycles and unstable chaotic trajectories can all be stabilized using such control which is effective both for maps and flows. The control is of particular significance for systems with several degrees of freedom, as knowledge of only one variable on the desired unstable orbit is sufficient to settle the system onto that orbit. We find in all cases that the transient time is a decreasing function of the stiffness of control. But increasing the stiffness beyond an optimum value can increase the transient time. We have also used such a mechanism to control spatiotemporal chaos is a well-known coupled map lattice model.     

Stochastic resonance in time-delayed bistable systems driven by weak periodic signal

We study theoretically a bistable system with time-delayed feedback driven by a weak periodic force. The effective potential function and the steady-state probability density are derived. The delay time and the strength of its feedback can change the shapes of the potential wells. In the adiabatic approximation, the signal-to-noise ratio (SNR) of the system with a weak periodic force is obtained. The time-delayed feedback modulates the magnitude of SNR by changing the shape of the potential and the effective strength of the signal. The maximum of SNR decreases with increasing the feedback intensity ?. When ? is negative (or positive), the time delay can suppress (or promote) the stochastic resonance phenomenon.     

分数阶时滞反馈对Duffing振子动力学特性的影响

研究了含分数阶时滞耦合反馈的Duffing自治系统, 通过平均法得到了系统周期解的一阶近似解析形式, 定义了以反馈系数、分数阶阶次、时滞参数表示的等效刚度和等效阻尼系数, 发现分数阶时滞耦合反馈同时具有速度时滞反馈和位移时滞反馈的作用. 比较了三种参数条件下近似解析解与数值积分的结果, 二者的吻合精度都很高, 证明了近似解析解的正确性和准确性. 分析了反馈系数、分数阶阶次和非线性刚度系数等参数对系统分岔点、周期解稳定性、周期解的存在范围、零解的稳定性以及稳定性切换次数等系统动力学特性的影响.     

Delayed feedback for controlling the nature of bifurcations in friction-induced vibrations

We analyse the control of friction-induced vibrations using time-delayed displacement feedback. We have used the exponential model for the drooping characteristics of the friction force for which the bifurcation is subcritical in nature. With an appropriate choice of the control parameters we have managed to change the nature of the bifurcation to supercritical along with increasing the stability boundaries. A nonlinear controller is required when the control force is applied in a direction parallel to the friction force. In contrast, a linear time-delayed displacement feedback applied in a direction normal to the friction force achieves our dual objective of controlling the nature of the bifurcation as well as quenching the vibrations. We also consider a dynamic friction model (the LuGre model) and observe that the qualitative change in the nature of the bifurcation is independent of the complexity considered in modeling the friction force.     

Seismic test of least-input-energy control with ground velocity feedback for variable-stiffness isolation systems

A variable-stiffness isolation system, whose isolation stiffness can be altered instantaneously in response to the seismic load, is able to provide better seismic protection for vibration-sensitive equipment or facilities than a conventional isolation system with a fixed stiffness. To determine its time-variant isolation stiffness, this system usually requires an effective on-line control law. In this study, a control strategy called the least input energy control (LIEC) is proposed for a general variable-stiffness isolation system. With the feedback of the ground velocity, at each time step the LIEC is able to determine the optimal isolation stiffness that minimizes the input seismic energy transmitted onto the isolated object. In order to evaluate its control performance, the LIEC was physically implemented on a leverage-type variable-stiffness isolation system, and tested in a seismic simulation test. The experimental response of the LIEC was then compared to the uncontrolled response, as well as the simulated responses of two semi-active control laws derived from the widely used LQR control and modal control. A comparison of the results demonstrates that, among all the control cases considered, the LIEC transmits the least seismic input energy to the isolated system, and thus has the best isolation performance. In addition, the test data also show that the LIEC requires the least control force and control energy. This indicates that the LIEC is also a very efficient control method for variable-stiffness isolation systems.