Non-resonant and resonant chaotic dynamics in externally excited cyclic systems

DOI10.1007/BF01181808zbMath1068.70025OpenAlexW4248747761MaRDI QIDQ5952208

Geetha Samaranayake, Anil K. Bajaj, S. Samaranayake

Publication date: 2001

Published in: Acta Mechanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01181808

zbMATH Keywords

homoclinic orbitsHamiltonian perturbationshigher-dimensional Melnikov method

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Chaotic behavior of solutions to dynamical problems in solid mechanics (74H65) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09)

Related Items (8)

Global bifurcations of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation ⋮ Multi-pulse jumping orbits and homoclinic trees in motion of a simply supported rectangular metallic plate ⋮ Global bifurcations and homoclinic trees in motion of a thin rectangular plate on a nonlinear elastic foundation ⋮ Orbits homoclinic to resonances in a harmonically excited and undamped circular plate ⋮ Global bifurcations and chaos in externally excited cyclic systems ⋮ Global bifurcations of a taut string with 1:2 internal resonance ⋮ Global bifurcations and single‐pulse homoclinic orbits of a plate subjected to the transverse and in‐plane excitations ⋮ Global bifurcations and chaos of a composite laminated cylindrical shell in supersonic air flow

Cites Work

• Unnamed Item
• Unnamed Item
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Resonant motion of a spherical pendulum
• Global bifurcations and chaos. Analytical methods
• Dynamics of a nonlinear periodic structure with cyclic symmetry
• Orbits homoclinic to resonances, with an applications to chaos in a model of the forced and damped sine-Gordon equation
• On the existence of chaos in a class of two-degree-of-freedom, damped, strongly parametrically forced mechanical systems with broken \(O(2)\) symmetry
• Orbits homoclinic to resonances: The Hamiltonian case
• Nonlinear dynamics of a shallow arch under periodic excitation. II: 1:1 internal resonance
• Nonlinear dynamics of a shallow arch under periodic excitation. I: 1:2 internal resonance
• Amplitude modulated chaos in two-degree-of-freedom systems with quadratic nonlinearities
• Amplitude modulated dynamics and bifurcations in the resonant response of a structure with cyclic symmetry
• Global bifurcation and chaos in parametrically forced systems with one-one resonance
• On the amplitude dynamics and crisis in resonant motion of stretched strings
• Modal Interactions in Dynamical and Structural Systems

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