Transitions from localization to nonlocalization in strongly nonlinear damped oscillators

DOI10.1016/S0960-0779(99)00076-4zbMath0965.70034OpenAlexW2081966756MaRDI QIDQ1573290

Alexander F. Vakakis, Oleg V. Gendelman

Publication date: 5 August 2001

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0960-0779(99)00076-4

zbMATH Keywords

bifurcationlocalizationtransition pointdirect numerical integrationsnonlocalizationstrongly nonlinear damped oscillators

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Bifurcations and instability for nonlinear problems in mechanics (70K50)

Related Items (7)

Transient mode localization in coupled strongly nonlinear exactly solvable oscillators ⋮ Confinement of Vibrations in Flexible Structures Using Supplementary Absorbers: Dynamic Optimization ⋮ Oscillator with a sum of noninteger-order nonlinearities ⋮ Competitive energy transfer between a two degree-of-freedom dynamic system and an absorber with essential nonlinearity ⋮ Nonlinear asymptotic analysis of a system of two free coupled oscillators with cubic nonlinearities ⋮ Unidirectional energy transport in the symmetric system of non-linearly coupled oscillators and oscillatory chains ⋮ Reflection of short rectangular pulses in the ideal string attached to strongly nonlinear oscillator

Cites Work

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• Slow periodic crossing of a pitchfork bifurcation in an oscillating system
• Transitions from strongly to weakly nonlinear motions of damped nonlinear oscillators
• A Multiple-Scales Analysis of Nonlinear, Localized Modes in a Cyclic Periodic System
• The 𝐴𝑡𝑒𝑏(ℎ)-functions and their properties
• Generation of Localization in a Discrete Chain with Periodic Boundary Conditions: Numerical and Analytical Results

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