VIBRATION ANALYSIS OF A SELF-EXCITED SYSTEM WITH PARAMETRIC FORCING AND NONLINEAR STIFFNESS

DOI10.1142/S021812749900033XzbMath0947.70014MaRDI QIDQ4941662

Grzegorz Litak, Kazimierz Szabelski, Jerzy Warminski, Grzegorz Spuz-Szpos

Publication date: 13 March 2000

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

zbMATH Keywords

stabilityLyapunov exponentsFloquet theorymultiple-time scale methodparametric excitation with nonlinear stiffnessvibration synchronization

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Forced motions for nonlinear problems in mechanics (70K40) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Parametric resonances for nonlinear problems in mechanics (70K28)

Related Items (7)

Existence of quasi-periodic solutions of fast excited van der Pol-Mathieu-Duffing equation ⋮ Transition to chaos in the self-excited system with a cubic double well potential and parametric forcing ⋮ Unnamed Item ⋮ Chaotic combustion in spark ignition engines ⋮ Chaotic vibration of a quarter-car model excited by the road surface profile ⋮ The damping term makes the Smale-horseshoe heteroclinic chaotic motion easier ⋮ Dynamical Response of a Van der Pol System with an External Harmonic Excitation and Fractional Derivative

Cites Work

• Chaos in limit cycle systems with external periodic excitations
• A perturbation method for the analysis of vibrations and bifurcations associated with non-autonomous systems. I: Non-resonance case
• A perturbation method for the analysis of vibrations and bifurcations associated with non-autonomous systems. II: Resonance case
• Parametric self-excited nonlinear system vibrations analysis with inertial excitation
• Transition to chaos in a generalized van der Pol's equation

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