Bionic Structure Inspired by Tree Frogs to Enhance Damping Performance.

Magnetic fluid shock absorbers (MFSAs) have been successfully utilized to eliminate microvibrations of flexible spacecraft structures. The method of enhancing the damping efficiency of MFSAs has always been a critical issue. To address this, we drew inspiration from the tree frog's toe pads, which exhibit strong friction due to their unique surface structure. Using 3D printing, we integrated bionic textures copied from tree frog's toe pad surfaces onto MFSAs, which is the first time to combine bionic design and MFSAs. Additionally, this is also the first time that surface textures have been applied to MFSAs. However, we also had to consider practical engineering applications and manufacturing convenience, so we modified the shape of bionic textures. To do so, we used an edge extraction algorithm for image processing and obtained recognition results. After thorough consideration, we chose hexagon as the shape of surface textures instead of bionic textures. For theoretical analysis, a magnetic field-flow field coupling dynamic model for MFSAs was built for the first time to simulate the magnetic fluid (MF) flow in one oscillation cycle. Using this model, the flow rate contours of the MF were obtained. It was observed that textures cause vortexes to form in the MF layer, which produced an additional velocity field. This increased the shear rate, ultimately leading to an increase in flow resistance. Finally, we conducted vibration reduction experiments and estimated damping characteristics of the proposed MFSAs to prove the effectiveness of both bionic texture and hexagon surface textures. Fortunately, we concluded that hexagon surface textures not only improve the damping efficiency of MFSAs but also require less MF mass.

Invisible grazings and dangerous bifurcations in impacting systems: the problem of narrow-band chaos.

We discovered a narrow band of chaos close to the grazing condition for a simple soft impact oscillator. The phenomenon was observed experimentally for a range of system parameters. Through numerical stability analysis, we argue that this abrupt onset to chaos is caused by a dangerous bifurcation in which two unstable period-3 orbits, created at "invisible" grazings, take part.

Analysis and control of the dynamical response of a higher order drifting oscillator.

This paper studies a position feedback control strategy for controlling a higher order drifting oscillator which could be used in modelling vibro-impact drilling. Special attention is given to two control issues, eliminating bistability and suppressing chaos, which may cause inefficient and unstable drilling. Numerical continuation methods implemented via the continuation platform COCO are adopted to investigate the dynamical response of the system. Our analyses show that the proposed controller is capable of eliminating coexisting attractors and mitigating chaotic behaviour of the system, providing that its feedback control gain is chosen properly. Our investigations also reveal that, when the slider's property modelling the drilled formation changes, the rate of penetration for the controlled drilling can be significantly improved.

Basins of attraction of the bistable region of time-delayed cutting dynamics.

This paper investigates the effects of bistability in a nonsmooth time-delayed dynamical system, which is often manifested in science and engineering. Previous studies on cutting dynamics have demonstrated persistent coexistence of chatter and chatter-free responses in a bistable region located in the linearly stable zone. As there is no widely accepted definition of basins of attraction for time-delayed systems, bistable regions are coined as unsafe zones (UZs). Hence, we have attempted to define the basins of attraction and stability basins for a typical delayed system to get insight into the bistability in systems with time delays. Special attention was paid to the influences of delayed initial conditions, starting points, and states at time zero on the long-term dynamics of time-delayed systems. By using this concept, it has been confirmed that the chatter is prone to occur when the waviness frequency in the workpiece surface coincides with the effective natural frequency of the cutting process. Further investigations unveil a thin "boundary layer" inside the UZ in the immediate vicinity of the stability boundary, in which we observe an extremely fast growth of the chatter basin stability. The results reveal that the system is more stable when the initial cutting depth is smaller. The physics of the tool deflection at the instant of the tool-workpiece engagement is used to evaluate the cutting safety, and the safe level could be zero when the geometry of tool engagement is unfavorable. Finally, the basins of attraction are used to quench the chatter by a single strike, where the resultant "islands" offer an opportunity to suppress the chatter even when the cutting is very close to the stability boundary.

Archetypal oscillator for smooth and discontinuous dynamics.

We propose an archetypal system to investigate transitions from smooth to discontinuous dynamics. In the smooth regime, the system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. At the discontinuous limit, however, there is a substantial departure in the dynamics from the standard one. In particular, the velocity flow suffers a jump in crossing from one well to another, caused by the loss of local hyperbolicity due to the collapse of the stable and unstable manifolds of the stationary state. In the presence of damping and external excitation, the system has coexisting attractors and also a chaotic saddle which becomes a chaotic attractor when a smoothness parameter drops to zero. This attractor can bifurcate to a high-period periodic attractor or a chaotic sea with islands of quasiperiodic attractors depending on the strength of damping.

Two-dimensional map for impact oscillator with drift.

An impact oscillator with drift is considered. The model accounts for viscoelastic impacts and is capable of mimicking the dynamics of progressive motion, which is important in many applications. To simplify the analysis of this system, a transformation decoupling the original coordinates is introduced. As a result, the bounded oscillations are separated from the drift motion. To study the bounded dynamics, a two-dimensional analytical map is developed and analyzed. In general, the dynamic state of the system is fully described by four variables: time tau , relative displacement p and velocity y of the mass, and relative displacement q of the slider top. However, this number can be reduced to two if the beginning of the progression phase is being monitored. The lower and upper bounds of the map domain are approximated. A graphical method of iteration of the two-dimensional map, similar to the cobweb method used in the one-dimensional case, is proposed. The results of numerical iterations of this two-dimensional map are presented, and a comparison is given between bifurcation diagrams calculated for this map and for the original system of differential equations.

Intermittent control of coexisting attractors.

This paper proposes a new control method applicable for a class of non-autonomous dynamical systems that naturally exhibit coexisting attractors. The central idea is based on knowledge of a system's basins of attraction, with control actions being applied intermittently in the time domain when the actual trajectory satisfies a proximity constraint with regards to the desired trajectory. This intermittent control uses an impulsive force to perturb one of the system attractors in order to switch the system response onto another attractor. This is carried out by bringing the perturbed state into the desired basin of attraction. The method has been applied to control both smooth and non-smooth systems, with the Duffing and impact oscillators used as examples. The strength of the intermittent control force is also considered, and a constrained intermittent control law is introduced to investigate the effect of limited control force on the efficiency of the controller. It is shown that increasing the duration of the control action and/or the number of control actuations allows one to successfully switch between the stable attractors using a lower control force. Numerical and experimental results are presented to demonstrate the effectiveness of the proposed method.

Excitement and synchronization of small-world neuronal networks with short-term synaptic plasticity.

Excitement and synchronization of electrically and chemically coupled Newman-Watts (NW) small-world neuronal networks with a short-term synaptic plasticity described by a modified Oja learning rule are investigated. For each type of neuronal network, the variation properties of synaptic weights are examined first. Then the effects of the learning rate, the coupling strength and the shortcut-adding probability on excitement and synchronization of the neuronal network are studied. It is shown that the synaptic learning suppresses the over-excitement, helps synchronization for the electrically coupled network but impairs synchronization for the chemically coupled one. Both the introduction of shortcuts and the increase of the coupling strength improve synchronization and they are helpful in increasing the excitement for the chemically coupled network, but have little effect on the excitement of the electrically coupled one.

Transient tumbling chaos and damping identification for parametric pendulum.

The aim of this study is to provide a simple, yet effective and generally applicable technique for determining damping for parametric pendula. The proposed model is more representative of system dynamics because the numerical results describe the qualitative features of experimentally exhibited transient tumbling chaotic motions well. The assumption made is that the system is accurately modelled by a combination of viscous and Coulomb dampings; a parameter identification procedure is developed from this basis. The results of numerical and experimental time histories of free oscillations are compared with the model produced from the parameters identified by the classic logarithmic decrement technique. The merits of the present method are discussed before the model is verified against experimental results. Finally, emphasis is placed on a close corroboration between the experimental and theoretical transient tumbling chaotic trajectories.

Hysteretic effects of dry friction: modelling and experimental studies.

In this paper, the phenomena of hysteretic behaviour of friction force observed during experiments are discussed. On the basis of experimental and theoretical analyses, we argue that such behaviour can be considered as a representation of the system dynamics. According to this approach, a classification of friction models, with respect to their sensitivity on the system motion characteristic, is introduced. General friction modelling of the phenomena accompanying dry friction and a simple yet effective approach to capture the hysteretic effect are proposed. Finally, the experimental results are compared with the numerical simulations for the proposed friction model.

Experimental study of impact oscillator with one-sided elastic constraint.

In this paper, extensive experimental investigations of an impact oscillator with a one-sided elastic constraint are presented. Different bifurcation scenarios under varying the excitation frequency near grazing are shown for a number of values of the excitation amplitude. The mass acceleration signal is used to effectively detect contacts with the secondary spring. The most typical recorded scenario is when a non-impacting periodic orbit bifurcates into an impacting one via grazing mechanism. The resulting orbit can be stable, but in many cases it loses stability through grazing. Following such an event, the evolution of the attractor is governed by a complex interplay between smooth and non-smooth bifurcations. In some cases, the occurrence of coexisting attractors is manifested through discontinuous transition from one orbit to another through boundary crisis. The stability of non-impacting and impacting period-1 orbits is then studied using a newly proposed experimental procedure. The results are compared with the predictions obtained from standard theoretical stability analysis and a good correspondence between them is shown for different stiffness ratios. A mathematical model of a damped impact oscillator with one-sided elastic constraint is used in the theoretical studies.

Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics.

In a recent paper we examined a model of an arch bridge with viscous damping subjected to a sinusoidally varying central load. We showed how this yields a useful archetypal oscillator which can be used to study the transition from smooth to discontinuous dynamics as a parameter, alpha, tends to zero. Decreasing this smoothness parameter (a non-dimensional measure of the span of the arch) changes the smooth load-deflection curve associated with snap-buckling into a discontinuous sawtooth. The smooth snap-buckling curve is not amenable to closed-form theoretical analysis, so we here introduce a piecewise linearization that correctly fits the sawtooth in the limit at alpha=0. Using a Hamiltonian formulation of this linearization, we derive an analytical expression for the unperturbed homoclinic orbit, and make a Melnikov analysis to detect the homoclinic tangling under the perturbation of damping and driving. Finally, a semi-analytical method is used to examine the full nonlinear dynamics of the perturbed piecewise linear system. A chaotic attractor located at alpha=0.2 compares extremely well with that exhibited by the original arch model: the topological structures are the same, and Lyapunov exponents (and dimensions) are in good agreement.