scholarly journals Phase-locking between Kuramoto oscillators: Robustness to time-varying natural frequencies

2010 ◽  
Author(s):  
Alessio Franci ◽  
Antoine Chaillet ◽  
William Pasillas-Lepine
Keyword(s):  
Natural Frequencies ◽  
Phase Locking ◽  
Time Varying ◽  
Kuramoto Oscillators

scholarly journals Analysis of Dynamic Characteristics of a Propeller Blade Subjected to Large Material Removal in Milling

2020 ◽  
pp. 10-14
Author(s):  
Luyi Han ◽  
◽  
Riliang Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Behavior ◽  
Dynamic Characteristics ◽  
Material Removal ◽  
Natural Frequencies ◽  
Machining Process ◽  
Time Varying ◽  
Propeller Blade ◽  
Large Material

A propeller blade, as a typical example of low-rigidity components, is prone to chatter and deformation in machining process, especially when large material removal is applied. In order to foresee the problems and then optimize the process, identification of the dynamic behavior of the workpiece is of great importance. This paper studies the dynamic characteristics of the workpiece in the machining process from plate to propeller blade using Finite Element Method. The results show that the time-varying natural frequencies of the workpiece decrease gradually at the beginning steps of the process due to the influence of material removal, and increases afterwards influenced by the geometry of the blade.

scholarly journals The conditions of full synchronization in generalized Kuramoto models [in Polish: Warunki pełnej synchronizacji w uogólnionych modelach Kuramoto]

2020 ◽  
Author(s):  
Jeremi Ochab
Keyword(s):  
Coupled Oscillators ◽  
Discrete System ◽  
Natural Frequencies ◽  
Phase Locking ◽  
Finite Size ◽  
Kuramoto Model ◽  
Winding Number ◽  
Critical Coupling ◽  
General Phase ◽  
Full Synchronization

A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and numerically that finite-size systems may have many different synchronized stable solutions which are characterised by different values of the winding number. The lower bound for the critical coupling $k_c$ is given, as well as an algorithm for its exact calculation. It is shown that in general phase-locking does not lead to phase coherence in 1D.

scholarly journals Spike-Firing Resonance in Hypoglossal Motoneurons

2008 ◽  
Vol 99 (6) ◽  
pp. 2916-2928 ◽  
Author(s):  
Johannes F. M. van Brederode ◽  
Albert J. Berger
Keyword(s):  
High Reliability ◽  
Phase Locking ◽  
Sine Wave ◽  
Spike Timing ◽  
Oscillatory Activity ◽  
Time Varying ◽  
Locking Range ◽  
Spike Firing ◽  
40 Hz

During an inspiration the output of hypoglossal (XII) motoneurons (HMs) in vitro is characterized by synchronous oscillatory firing in the 20- to 40-Hz range. To maintain synchronicity it is important that the cells fire with high reliability and precision. It is not known whether the intrinsic properties of HMs are tuned to maintain synchronicity when stimulated with time-varying inputs. We intracellularly recorded from HMs in an in vitro brain stem slice preparation from juvenile mice. Cells were held at or near spike threshold and were stimulated with steady or swept sine-wave current functions (10-s duration; 0- to 40-Hz range). Peristimulus time histograms were constructed from spike times based on threshold crossings. Synaptic transmission was suppressed by including blockers of GABAergic, glycinergic, and glutamatergic neurotransmission in the bath solution. Cells responded to sine-wave stimulation with bursts of action potentials at low (<3- to 5-Hz) sine-wave frequency, whereas they phase-locked 1:1 to the stimulus at intermediate frequencies (3–25 Hz). Beyond the 1:1 frequency range cells were able to phase-lock to subharmonics (1:2, 1:3, or 1:4) of the input frequency. The 1:1 phase-locking range increased with increasing stimulus amplitude and membrane depolarization. Reliability and spike-timing precision were highest when the cells phase-locked 1:1 to the stimulus. Our findings suggest that the coding of time-varying inspiratory synaptic inputs by individual HMs is most reliable and precise at frequencies that are generally lower than the frequency of the synchronous inspiratory oscillatory activity recorded from the XII nerve.

scholarly journals Controlling synchrony in a network of Kuramoto oscillators with time-varying coupling

2015 ◽  
Vol 301-302 ◽  
pp. 36-47 ◽  
Author(s):  
Rachel Leander ◽  
Suzanne Lenhart ◽  
Vladimir Protopopescu
Keyword(s):  
Time Varying ◽  
Kuramoto Oscillators

scholarly journals Time-Varying Total Stiffness Matrix of a Rigid Machine Spindle-Angular Contact Ball Bearings Assembly: Theory and Analytical/Experimental Verifications

2011 ◽  
Vol 18 (5) ◽  
pp. 641-670 ◽  
Author(s):  
Fawzi M.A. El-Saeidy
Keyword(s):  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Time Dependent ◽  
Time Varying ◽  
Ball Bearings ◽  
Rigid Rotor ◽  
Bearing Stiffness ◽  
Machine Spindle ◽  
Matrix Case

A lagrangian formulation is presented for the total dynamic stiffness and damping matrices of a rigid rotor carrying noncentral rigid disk and supported on angular contact ball bearings (ACBBs). The bearing dynamic stiffness/damping marix is derived in terms of the bearing motions (displacements/rotations) and then the principal of virtual work is used to transfer it from the bearing location to the rotor mass center to obtain the total dynamic stiffness/damping matrix. The bearing analyses take into account the bearing nonlinearities, cage rotation and bearing axial preload. The coefficients of these time-dependent matrices are presented analytically. The equations of motion of a rigid rotor-ACBBs assembly are derived using Lagrange's equation. The proposed analyses on deriving the bearing stiffness matrix are verified against existing bearing analyses of SKF researchers that, in turn, were verified using both SKF softwares/experiments and we obtained typical agreements. The presented total stiffness matrix is applied to a typical grinding machine spindle studied experimentally by other researchers and excellent agreements are obtained between our analytical eigenvalues and the experimental ones. The effect of using the total full stiffness matrix versus using the total diagonal stiffness matrix on the natural frequencies and dynamic response of the rigid rotor-bearings system is studied. It is found that using the diagonal matrix affects natural frequencies values (except the axial frequency) and response amplitudes and pattern and causes important vibration tones to be missig from the response spectrum. Therefore it is recommended to use the full total stiffness matrix and not the diagonal matrix in the design/vibration analysis of these rotating machines. For a machine spindle-ACBBs assembly under mass unbalnce and a horizontal force at the spindle cutting nose when the bearing time-varying stiffness matrix (bearing cage rotation is considered) is used, the peak-to-valley variation in time domain of the stiffness matrix elements becomes significant compared to its counterpart when the bearing standard stiffness matrix (bearing cage rotation is neglected) is used. The vibration spectrum of the time-varying matrix case is marked by tones at bearing outer ring ball passing frequency, rotating unbalnce frequency and combination compared to spectrum of the standard stiffness matrix case which is marked by only the rotating unbalnce frequency. Therfore, it is highly recomended to model bearing stiffness matrix to be a time-dependent.

scholarly journals Experimental Dynamic Analysis of Nonlinear Beams under Moving Loads

2012 ◽  
Vol 19 (5) ◽  
pp. 969-978 ◽  
Author(s):  
A. Bellino ◽  
S. Marchesiello ◽  
L. Garibaldi
Keyword(s):  
Natural Frequencies ◽  
Linear Time ◽  
Moving Load ◽  
Nonlinear Effects ◽  
Experimental Tests ◽  
Interesting Case ◽  
Reinforced Concrete Beams ◽  
Nonlinear Behaviour ◽  
Time Varying ◽  
Over Time

It is well known that nonlinear systems, as well as linear time-varying systems, are characterized by non-stationary response signals. In this sense, they both show natural frequencies that are not constant over time; this variation has however different origins: for a time-varying system the mass, and possibly the stiffness distributions, are changing over time, while for a nonlinear system the natural frequencies are amplitude-dependent. An interesting case of time-varying system occurs when analyzing the transit of a train over a railway bridge, easily simulated by the crossing of a moving load over a beam. In this case, the presence of a nonlinearity in the beam behaviour can cause a significant alteration of the modal parameters extracted from the linearized model, such that the contributions of the two effects are no more distinguishable.For this study, some reinforced concrete beams have been tested in the framework of a vast project: these beams show a clear softening nonlinear behaviour, well detectable when the excitation is produced by a hammer (free response). If the passage of a carriage is considered, moreover, the variation of natural frequencies is always larger than expected because of this softening nonlinearity.The article first analyzes theoretically the two effects on the natural frequencies of a simply supported beam, then a numerical and an experimental tests are presented. The identification procedure is conducted with a linear algorithm called ST-SSI, which has been demonstrated to be appropriate for the analysis of non-stationary signals, in particular in presence of moving masses. The article shows that the nonlinear contribution can be well estimated by using this linear tool but, on the contrary, when also moving masses are present, it is difficult to separate the nonlinear effects from the time varying ones.

Time-Varying Transmissibility Analysis of Vehicle–Bridge Interaction Systems with Application to Bridge-Friendly Vehicles

2021 ◽  
Author(s):  
Ke Lin ◽  
Chin An Tan ◽  
Chengqiang Ge ◽  
Huancai Lu
Keyword(s):  
Natural Frequencies ◽  
Control Strategies ◽  
Structural Parameters ◽  
A Priori ◽  
Coupled System ◽  
Parameter Tuning ◽  
Effective Control ◽  
Time Varying ◽  
Time Frequency ◽  
Tuning Strategy

It is well known that the natural frequencies of a coupled vehicle–bridge interaction system are time-varying. While this knowledge is useful for applications in bridge health monitoring, it does not provide an understanding of the relations between the excitation and coupled system responses, nor leads to developments of effective control strategies to mitigate vibration. In this paper, a novel theoretical framework for the time-varying displacement transmissibility is developed using a time-frozen technique. The time–frequency characteristics of the transmissibility functions are investigated to gain fundamental understanding and insights of the coupling dynamics in relation to the matching of bridge and vehicle natural frequencies. An important aspect of the transmissibility formulation is that it leads to the development of physics-based vibration control strategies in the frequency domain. By applying the principle of fixed points from vibration absorber designs to the transmissibility functions, an optimally tuned vehicle suspension to mitigate bridge vibration is obtained. The tuning strategy depends only on a priori known structural parameters. Thus, the tuning strategy provides useful guidelines in practice and is shown to be effective in reducing the vibrations of both the moving vehicle and the bridge. This work paves a foundation for further research in the design of bridge-friendly vehicles via parameter tuning.

scholarly journals Influence of the Eccentric Error of Star Gear on the Bifurcation Properties of Herringbone Star Gear Transmission with Floating Sun Gear

2018 ◽  
Vol 2018 ◽  
pp. 1-32
Author(s):  
Fang Guo ◽  
Zongde Fang ◽  
Xijin Zhang ◽  
Yanmei Cui
Keyword(s):  
Load Balancing ◽  
Numerical Method ◽  
Dynamic Model ◽  
Phase Plane ◽  
Natural Frequencies ◽  
Rotation Frequency ◽  
Gear Transmission ◽  
Time Varying ◽  
Bifurcation Diagrams ◽  
Mesh Stiffness

Taking a herringbone star gear transmission (HSGT) with floating sun gear as an example, the system bifurcation characteristics with the changing of the eccentric error of star gear and the working frequencies are analyzed. For this analysis, a generalized dynamic model of HSGT considering the manufacturing eccentric errors, time-varying mesh stiffness, and load balancing mechanism is established and solved by numerical method. The floating process of sun gear is explained. In this paper, there are seven cases about the eccentric errors of star gears which are calculated, respectively. To study the effect of the working frequencies (including meshing frequency and rotation frequency), the calculation is done at three kinds of input speed in which the working frequencies are close to the system natural frequencies. The results are demonstrated in detail by the bifurcation diagrams, phase plane plots, and Poincare maps. The system bifurcation characteristics are particularly analyzed and compared in every case. This work provides important guidance to the engineering of HSGT.

Research on Dynamics of Double-Mesh Helical Gear Set

2012 ◽  
Vol 215-216 ◽  
pp. 1021-1025 ◽  
Author(s):  
Fu Chun Yang ◽  
Qi Lin Huang ◽  
Yong Wang ◽  
Jun Gang Wang
Keyword(s):  
Natural Frequencies ◽  
Vibration Mode ◽  
Helical Gear ◽  
Dynamic Responses ◽  
Time Varying ◽  
Sensitive Area ◽  
Axial Vibration ◽  
Mesh Stiffness ◽  
Natural Modes ◽  
Rotational Vibration

A dynamic model of double-mesh helical gear set was established including the torsional vibration, axial vibration and time varying mesh stiffness. The natural modes were systematically analyzed and classified into three types: rotational vibration mode, axial vibration mode and overall vibration mode. The influence of time varying mesh stiffness and the dynamic responses of the gear set were also investigated. The results showed that several natural frequencies are excited in the dynamic response and there is a frequency sensitive area which may cause large dynamic load.

scholarly journals Formation, stability and basin of phase-locking for Kuramoto oscillators bidirectionally coupled in a ring

2018 ◽  
Vol 13 (2) ◽  
pp. 323-337
Author(s):  
Xiaoxue Zhao ◽  
◽  
Zhuchun Li ◽  
Xiaoping Xue ◽  
Keyword(s):  
Phase Locking ◽  
Kuramoto Oscillators
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