Amplitude modulated dynamics and bifurcations in the resonant response of a structure with cyclic symmetry

DOI10.1007/BF01176819zbMath0862.70018OpenAlexW2002263341MaRDI QIDQ1914324

S. Samaranayake, Anil K. Bajaj, Osita D. I. Nwokhah

Publication date: 4 June 1997

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

Full work available at URL: https://doi.org/10.1007/bf01176819

zbMATH Keywords

travelling wavesaveraging methodchaotic amplitude modulationsmultiple chaotic attractorsspatially distributed harmonic excitationweakly nonlinear springs

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Local and nonlocal bifurcation theory for dynamical systems (37G99) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items

Vibration absorbers for a rotating flexible structure with cyclic symmetry: nonlinear path design ⋮ Non-resonant and resonant chaotic dynamics in externally excited cyclic systems ⋮ Global bifurcations and chaos in externally excited cyclic systems ⋮ Resonant vibrations in harmonically excited weakly coupled mechanical systems with cyclic symmetry

Uses Software

• AUTO
• AUTO-86

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Resonant motion of a spherical pendulum
• Bifurcations in a model of magnetoconvection
• Local and global behavior near homoclinic orbits
• Miles' evolution equations for axisymmetric shells: Simple strange attractors in structural dynamics
• Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. I: Theory
• Global bifurcations and chaos. Analytical methods
• Dynamics of a nonlinear periodic structure with cyclic symmetry
• Global bifurcations in the forced vibration of a damped string
• Amplitude modulated and chaotic dynamics in resonant motion of strings
• Resonantly forced surface waves in a circular cylinder
• Chaos in a Harmonically Excited Elastic Beam
• Excitation of Rotationally Periodic Structures
• On the amplitude dynamics and crisis in resonant motion of stretched strings
• Modal Interactions in Dynamical and Structural Systems
• Non-linear phenomena in forced vibrations of a nearly square plate: Antisymmetric case
• Crises, sudden changes in chaotic attractors, and transient chaos
• A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE

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