共查询到20条相似文献,搜索用时 0 毫秒
1.
K. Yagasaki 《Nonlinear dynamics》1996,9(4):391-417
We consider a pendulum subjected to linear feedback control with periodic desired motions. The pendulum is assumed to be driven by a servo-motor with small time constant, so that the feedback control system can be approximated by a periodically forced oscillator. It was previously shown by Melnikov's method that transverse homoclinic and heteroclinic orbits exist and chaos may occur in certain parameter regions. Here we study local bifurcations of harmonics and subharmonics using the second-order averaging method and Melnikov's method. The Melnikov analysis was performed by numerically computing the Melnikov functions. Numerical simulations and experimental measurements are also given and are compared with the previous and present theoretical predictions. Sustained chaotic motions which result from homoclinic and heteroclinic tangles for not only single but also multiple hyperbolic periodic orbits are observed. Fairly good agreement is found between numerical simulation and experimental results. 相似文献
2.
Hendrik Hölscher 《International Journal of Non》2007,42(4):608-625
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. 相似文献
3.
Kazuyuki Yagasaki 《Nonlinear dynamics》2017,87(4):2335-2343
External feedback control of microcantilevers was previously demonstrated to be one of promising techniques to develop high-performance noncontact atomic force microscopy, but it has a difficulty in reproducing oscillatory waveforms of fast vibrating microcantilevers. Here we propose an approach to overcome this difficulty by using approximate waveforms for vibrations of the cantilevers, instead of the actual ones, as control signals. The approximations are very simple and consist of the lowest frequency and constant components. We call the proposed technique, rough external feedback control, to distinguish it from the original one. The efficiency and validity of our approach are demonstrated by numerical simulations, and numerical bifurcation analyses are carried out. 相似文献
4.
A new class of models based on hysteresis functions is developed to describe the operation of dynamic mode atomic force microscopy.
Such models can account for dissipative phenomena affecting the interaction between the probe and the sample. The model analysis,
which is developed using frequency domain techniques, provides a insights into experimentally observed behavior. Experimental
data corroborates the models developed. 相似文献
5.
The size effect must be considered for dynamic modeling of an AFM since the dimensions of the AFM, are in micro-scale. In this study, a three-dimensional multi-scale method based on a non-classical continuum mechanic theory is developed in order to include material length scale parameter (MLSP) in the dynamic behavior of manipulation carried out by AFM. First, the governing equations of Macro Field (MF) are derived using the modified coupled stress theory and the Kirchhoff plate model. Moreover, Nano Field (NF) is modeled using the molecular dynamics equations. The MF and the NF are then combined employing the multi-scale algorithm. Rectangular and dagger cantilevers are taken into account to obtain manipulation results. The influence of two types of tip on the manipulation results is also investigated. The obtained results show that the deformations of the AFM components in non-classic models are less than the one in the classical model. Furthermore, Root Mean Square (RMS) results for a nano-particle demonstrates that damage and deformation of the nano-particle are underestimated by the classical model. The investigations carried out in the present study show the significance of employing the non-classical theory for analyzing AFM performance, particularly for estimation of separation time span. 相似文献
6.
In this paper, we investigate a low dimensional model of percussive drilling with vibro-impact to mimic the nonlinear dynamics of the bounded progression. Non- holonomity which arises in the stick-slip caused by the impact during drilling fails to be correctly identified via the classical techniques. A reduced model without non-holono- mity is derived by the introduction of a new state variable, of which averaging technique is employed successfully to detect the periodic motions. Local bifurcations are presented directly by using C-L method. Numerical simulations and the penetrating rate analysis along different choices of parame- ters have been carried out to probe the nonlinear behaviour and the optimal penetrating rate of the drilling system. 相似文献
7.
8.
A two-dimensional model is developed to study the flutter instability of a flag immersed in an inviscid flow. Two dimensionless parameters governing the system are the structure-to-fluid mass ratio M⁎ and the dimensionless incoming flow velocity U⁎. A transition from a static steady state to a chaotic state is investigated at a fixed M⁎=1 with increasing U⁎. Five single-frequency periodic flapping states are identified along the route, including four symmetrical oscillation states and one asymmetrical oscillation state. For the symmetrical states, the oscillation frequency increases with the increase of U⁎, and the drag force on the flag changes linearly with the Strouhal number. Chaotic states are observed when U⁎ is relatively large. Three chaotic windows are observed along the route. In addition, the system transitions from one periodic state to another through either period-doubling bifurcations or quasi-periodic bifurcations, and it transitions from a periodic state to a chaotic state through quasi-periodic bifurcations. 相似文献
9.
We consider the stochastic dynamics of an array of two closely spaced atomic force microscope cantilevers in a viscous fluid for use as a possible biomolecule sensor. The cantilevers are not driven externally, as is common in applications of atomic force microscopy, and we explore the stochastic cantilever dynamics due to the constant buffeting of fluid particles by Brownian motion. The stochastic dynamics of two adjacent cantilevers are correlated due to long range effects of the viscous fluid. Using a recently proposed thermodynamic approach the hydrodynamic correlations are quantified for precise experimental conditions through deterministic numerical simulations. Results are presented for an array of two readily available atomic force microscope cantilevers. It is shown that the force on a cantilever due to the fluid correlations with an adjacent cantilever is more than 3 times smaller than the Brownian force on an individual cantilever. Our results indicate that measurements of the correlations in the displacement of an array of atomic force microscopes can detect piconewton forces with microsecond time resolution. 相似文献
10.
We study the dynamical behavior of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever by a single mode approximation. The interaction between the sample and the cantilever is modeled by a Lennard--Jones potential which consists of a short-range repulsive potential and a long-range van der Waals (vdW) attractive potential. We analyze the dynamics of the cantilever sample system when the cantilever is subjected to a sinusoidal forcing. Using the Melnikov method, the region in the space of physical parameters where chaotic motion is present is determined. In addition, using a proportional and derivative controller, we compute the Melnikov function in terms of the parameters of the controller. Using this relation, controllers can be designed to selectively change the regime of dynamical interaction. 相似文献
11.
We study homoclinic behaviour in resonance zones of nonconservative,forced oscillators represented as one-parameter families of periodicperturbations of planar Hamiltonian systems. We use a Melnikov-typetechnique and obtain a simple condition under which separatrixsplittings with exponentially small upper bounds may occur. Todemonstrate our theory, we give two examples for Duffing-typeoscillators and compare the theoretical results with numericalsimulations. In these examples, homoclinic behaviour that was notreported in early work is detected. 相似文献
12.
13.
Manuel Iñarrea 《International Journal of Non》2006,41(1):86-100
We study the pitch motion dynamics of an asymmetric spacecraft in circular orbit under the influence of a gravity gradient torque. The spacecraft is perturbed by a small aerodynamic drag torque proportional to the angular velocity of the body about its mass center. We also suppose that one of the moments of inertia of the spacecraft is a periodic function of time. Under both perturbations, we show that the system exhibits a transient chaotic behavior by means of the Melnikov method. This method gives us an analytical criterion for heteroclinic chaos in terms of the system parameters which is numerically contrasted. We also show that some periodic orbits survive for perturbation small enough. 相似文献
14.
Ming Liu 《International Journal of Non》2008,43(6):521-526
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. 相似文献
15.
M. Kanerva J. Jokinen E. Sarlin O. Saarela 《International Journal of Solids and Structures》2013,50(20-21):3399-3405
This report describes investigations of grain boundary groove effects on mode II dominated interface fracture. The study focused on a specific interface between stainless steel and an epoxy adhesive. First, a finite element model was developed to simulate residual stresses and crack propagation. Second, the simulation results were compared with the experimental results from a previous study (Kanerva et al., 2013. Eng. Fract. Mech. 99, 147-158). Additional measurements were performed using atomic force microscopy. Based on the simulation, a 100-fold toughening effect due to the grain boundaries was determined. Implementation of flaws, in the form of interfacial voids, decreased the toughening effect by 35% and increased the mode II dominance significantly. The work underlines the practical importance of complete wetting by the adhesive and its necessary adherence to the grain boundary groove walls. 相似文献
16.
In this paper we search for the dynamics of a simple portal structure in the free and in the periodic excitation cases. By using the Center Manifold approach and Averaging Method, we obtain results on both stability and bifurcation of equilibrium points and periodic orbits. 相似文献
17.
In micro-manipulation, the adhesion force has very important influence on behaviors of micro-objects. Here, a theoretical study on the effects of humidity on the adhesion force is presented between atomic force microscope (AFM) tips and substrate. The analysis shows that the precise tip geometry plays a critical role on humidity depen- dence of the adhesion force, which is the dominant factor in manipulating micro-objects in AFM experiments. For a blunt (paraboloid) tip, the adhesion force versus humidity curves tends to the apparent contrast (peak-to-valley corrugation) with a broad range. This paper demonstrates that the abrupt change of the adhesion force has high correla- tion with probe curvatures, which is mediated by coordinates of solid-liquid-vapor contact lines (triple point) on the probe profiles. The study provides insights for further under- standing nanoscale adhesion forces and the way to choose probe shapes in manipulating micro-objects in AFM experiments. 相似文献
18.
一类慢变参数振子系统的同宿分叉及其安全盆侵蚀 总被引:2,自引:0,他引:2
分析一个具有慢变参数的非线性系统,利用Melnkov方法,分析了系统在参数发生变化时的同宿分叉,同时利用分叉结果,数值讨论了当系统参数发生变化时安全盆的侵蚀及分叉,混沌的联系。 相似文献
19.
This paper presents a detailed analysis on the dynamics of a delayed oscillator with negative damping and delayed feedback
control. Firstly, a linear stability analysis for the trivial equilibrium is given. Then, the direction of Hopf bifurcation
and stability of periodic solutions bifurcating from trivial equilibrium are determined by using the normal form theory and
center manifold theorem. It shows that with properly chosen delay and gain in the delayed feedback path, this controlled delayed
system may have stable equilibrium, or periodic solutions, or quasi-periodic solutions, or coexisting stable solutions. In
addition, the controlled system may exhibit period-doubling bifurcation which eventually leads to chaos. Finally, some new
interesting phenomena, such as the coexistence of periodic orbits and chaotic attractors, have been observed. The results
indicate that delayed feedback control can make systems with state delay produce more complicated dynamics. 相似文献
20.
The increasing threat raised by space debris led to the development of different mathematical models and approaches to investigate the dynamics of small particles orbiting around the Earth. The choice of such models and methods strongly depend on the altitude of the objects above Earth's surface, since the strength of the different forces acting on an Earth orbiting object (geopotential, atmospheric drag, lunar and solar attractions, solar radiation pressure, etc.) varies with the altitude of the debris.In this review, our focus is on presenting different analytical and numerical approaches employed in modern studies of the space debris problem. We start by considering a model including the geopotential, solar and lunar gravitational forces and the solar radiation pressure. We summarize the equations of motion using different formalisms: Cartesian coordinates, Hamiltonian formulation using Delaunay and epicyclic variables, Milankovitch elements. Some of these methods lead in a straightforward way to the analysis of resonant motions. In particular, we review results found recently about the dynamics near tesseral, secular and semi-secular resonances.As an application of the above methods, we proceed to analyze a timely subject, namely the possible causes for the onset of chaos in space debris dynamics. Precisely, we discuss the phenomenon of overlapping of resonances, the effect of a large area-to-mass ratio, the influence of lunisolar secular resonances.We conclude with a short discussion about the effect of the dissipation due to the atmospheric drag and we provide a list of minor effects, which could influence the dynamics of space debris. 相似文献