MELNIKOV'S METHOD AND STICK–SLIP CHAOTIC OSCILLATIONS IN VERY WEAKLY FORCED MECHANICAL SYSTEMS

DOI10.1142/S0218127499000341zbMath0947.70015OpenAlexW1988449047MaRDI QIDQ4941663

Mariusz Holicke, Jan Awrejcewicz

Publication date: 2 November 2000

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127499000341

zbMATH Keywords

frictionself-sustained oscillationsMelnikov's techniquequasi-autonomous oscillatorstick-slip chaotic dynamics

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Dynamical systems in classical and celestial mechanics (37N05)

Related Items (30)

ANALYTICAL ESTIMATES OF THE EFFECT OF NONLINEAR DAMPING IN SOME NONLINEAR OSCILLATORS ⋮ Experimental evidence of non-standard bifurcations in non-smooth oscillator dynamics ⋮ Analytical prediction of chaos in rotated Froude pendulum ⋮ Sliding bifurcations and chaos induced by dry friction in a braking system ⋮ Transition to chaos in the self-excited system with a cubic double well potential and parametric forcing ⋮ Analytical proof on the existence of chaos in a generalized Duffing-type oscillator with fractional-order deflection ⋮ Analytical prediction of stick-slip chaos in a double self-excited Duffing-type oscillator ⋮ Chaotic heteroclinic tangles with the degenerate Melnikov function ⋮ How to predict stick-slip chaos in \(R^4\) ⋮ Analytical estimates of the effect of amplitude modulated signal in nonlinearly damped Duffing-van der Pol oscillator ⋮ Frictional oscillations under the action of almost periodic excitation ⋮ Determination of the chaos onset in mechanical systems with several equilibrium positions ⋮ Threshold of Multiple Stick-Slip Chaos for an Archetypal Self-Excited SD Oscillator Driven by Moving Belt Friction ⋮ Melnikov method and detection of chaos for non-smooth systems ⋮ Random Disordered Periodical Input Induced Chaos in Discontinuous Systems ⋮ Melnikov theory for weakly coupled nonlinear RLC circuits ⋮ A rotating disk linked by a pair of springs ⋮ THE STUDY ON THE MIDSPAN DEFLECTION OF A BEAM BRIDGE UNDER MOVING LOADS BASED ON SD OSCILLATOR ⋮ STICK-SLIP DYNAMICS OF A TWO-DEGREE-OF-FREEDOM SYSTEM ⋮ Chaos prediction in the Duffing-type system with friction using Melnikov's function ⋮ A simplified optimal control method for homoclinic bifurcations ⋮ Estimation of chaotic and regular (stick-slip and slip-slip) oscillations exhibited by coupled oscillators with dry friction ⋮ Numerical computation of connecting orbits in planar piecewise smooth dynamical system ⋮ HETEROCLINIC BIFURCATIONS AND OPTIMAL CONTROL IN THE NONLINEAR ROCKING DYNAMICS OF GENERIC AND SLENDER RIGID BLOCKS ⋮ CHAOS IN NONAUTONOMOUS DIFFERENTIAL INCLUSIONS ⋮ BIFURCATIONS IN HYBRID MECHANICAL SYSTEMS WITH DISCONTINUITY BOUNDARIES ⋮ Melnikov's method for a general nonlinear vibro-impact oscillator ⋮ MECHANICAL MODELS OF CHUA'S CIRCUIT ⋮ ESTIMATION OF CHAOTIC THRESHOLDS FOR THE RECENTLY PROPOSED ROTATING PENDULUM ⋮ Melnikov-Type Chaos of Planar Systems with Two Discontinuities

Cites Work

• Models and computational methods for dynamic friction phenomena
• Some remarks on the stick-slip vibrations of a two degree-of-freedom mechanical model
• Bifurcations and chaos of a particular van der Pol-Duffing oscillator
• Stick-slip vibrations and chaos
• Chaotic Dynamics of Quasi-Periodically Forced Oscillators Detected by Melnikov’s Method
• NONLINEAR DYNAMICS OF A CLASS OF ANALOG-TO-DIGITAL CONVERTERS
• MECHANICAL STICK-SLIP VIBRATIONS

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