Abstract The existence and the nature of Hopf bifurcation is presented in delay-differential equation model so-called regenerative machine tool vibration. relevant nonlinearity considered at cutting force dependence on chip thickness. delayed terms show a special algebraic structure nonlinear part motion. This results surprisingly simple useful analytical formula end lengthy calculation based center manifold reduction corresponding infinite dimensional phase space. result gives way to...

This paper reviews the prediction of complex, unsteady and chaotic dynamics associated with material–cutting processes through nonlinear dynamical models. The status bifurcation phenomena such as subcritical Hopf instabilities is assessed. A new model using hysteresis in cutting force presented, which shown to exhibit complex quasi–periodic solutions. In addition, further evidence for non–regenerative polycarbonate plastic reviewed. authors draw conclusion that single–degree–of–freedom...

Velocity measurements and simulations in an idealized urban environment were studied, focusing on turbulent flow over street canyons. Time series of fluctuating velocities considered as marked point processes, the distribution mean residence times was characterized using a lognormal fit. The quadrant method applied to transform time into symbolic sequences, enabling investigation their information content. By analyzing word frequency normalized entropy levels, we compared measured simulated...

Abstract We study a binary tree-structured multi-degree-of-freedom nonlinear oscillator with impulsive and continuous excitations. The response of this model is studied for excitations that are applied to the largest masses. It shown how choosing mass smallest blocks influences system regarding dissipation efficient targeted energy transfer realized in system. simplified frequency plot introduced as means analyzing systems For excitations, it masses (nonlinear sinks) active only inside...

Mathematical models are essential for the design and control of offshore systems, to simulate fluid–structure interactions predict motions structural loads. In development derivation models, simplifying assumptions normally required, usually implying linear kinematics hydrodynamics. However, while assumption linear, small amplitude motion fits traditional problems, in normal operational conditions (it is desirable stabilize ships, boats, platforms), large potential dynamic instability may...

A simplified model of a container crane subject to delayed feedback is investigated. The conditions for Hopf bifurcation stable/unstable limit-cycle solutions are determined. It shown that subcritical unstable oscillations cannot be ruled out and the undesired coexistence stable large amplitude equilibrium endangers robustness time-delay control strategies. analyzed both analytically numerically using continuation method.

Persistence is defined as the probability that local value of a fluctuating field remains at particular state for certain amount time, before being switched to another state. The concept persistence has been found have many diverse practical applications, ranging from non-equilibrium statistical mechanics financial dynamics distribution time scales in turbulent flows and more. In this study, we carry out detailed analysis characteristics density functions (PDFs) velocity temperature...

Abstract Parametric excitation in the pitch/roll degrees of freedom (DoFs) can induce dynamic instability floating cylinder-type structures such as spar buoys, offshore wind or wave energy converters. At certain frequency and amplitude ranges input waves, parametric coupling between heave DoFs results undesirable large rotational motion. One possible remedy to mitigate existence resonance is use vibration absorbers. Two prominent types absorbers are tuned mass dampers (TMDs) nonlinear sinks...

Abstract A single-degree-of-freedom dynamic cutting fixture is used to map out a part of the lobed stability boundary in simple high-speed machining experiment. The experiment reveals hysteretic nature instability. 1 DOF mechanical model derived using parameters identified from We then show existence subcritical Hopf bifurcation this delay-differential equation which corresponds observed experimental calculation based on center manifold reduction. Then time domain simulation solve full...

Abstract The dynamics of a two-degrees-of-freedom (pitch–plunge) aeroelastic system is investigated. aerodynamic force modeled as piecewise linear function the effective angle attack. Conditions for admissible (existing) and virtual equilibria are determined. stability bifurcations analyzed. We find saddle-node, border collision rapid bifurcations. analysis shows that pitch–plunge model with simple approximation can reproduce transition from divergence to complex phenomenon stall flutter. A...

The classical Multiple Traveling Salesmen Problem is a well-studied optimization problem. Given set of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math>goals/targets and<mml:math id="M2"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:math>agents, the objective to find<mml:math id="M3"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:math>round trips, such that each target visited only once and by one agent, total distance of these...

Parametric resonance is a dynamic instability due to the internal transfer of energy between degrees freedom. known cause large unstable pitch and/or roll motions in floating bodies, and has been observed wave converters (WECs). The occurrence parametric can be highly detrimental performance WEC, since primary mode motion parasitically transferred into other modes, reducing available for conversion. In addition, oscillations produce increased loading on WEC structure mooring system,...

We study the dynamics of targeted energy transfers in suppressing chatter instability a single-degree-of-freedom (SDOF) machine tool system. The nonlinear regenerative (time-delayed) cutting force is main source vibrations (chatter). introduce an ungrounded sink (NES) coupled to tool, by which from NES and efficient dissipation can be realized during chatter. Studying variations transition curve with respect parameters, we analytically show that location Hopf bifurcation point influenced...