Dynamics of a parametrically excited system with two forcing terms

DOI10.3390/math2030172zbMath1307.70020OpenAlexW1965921066MaRDI QIDQ486027

Anastasia Sofroniou, Steven R. Bishop

Publication date: 14 January 2015

Published in: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3390/math2030172

zbMATH Keywords

parametric excitationquasiperiodicityroute to chaosdouble forcing

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Dynamical systems in classical and celestial mechanics (37N05) Parametric resonances for nonlinear problems in mechanics (70K28)

Related Items (3)

Unnamed Item ⋮ Stationary and non-stationary oscillatory dynamics of the parametric pendulum ⋮ Multistability and Hidden Attractors in the Dynamics of Permanent Magnet Synchronous Motor

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Periodic and quasiperiodic galloping of a wind-excited tower under external excitation
• Dynamics of the pendulum with periodically varying length
• Asymptotic solutions for a damped non-linear quasi-periodic Mathieu equation
• Strange attractors that are not chaotic
• Quasi-periodic oscillations, chaos and suppression of chaos in a nonlinear oscillator driven by parametric and external excitations
• Perturbation methods for bifurcation analysis from multiple nonresonant complex eigenvalues
• Stability region control for a parametrically forced Mathieu equation
• Quasi-periodic solutions and stability for a weakly damped nonlinear quasi-periodic Mathieu equation
• Multiple timescales analysis for 1:2 and 1:3 resonant Hopf bifurcations
• Locating bifurcations in quasiperiodically forced systems
• Symmetry-breaking in the response of the parametrically excited pendulum model
• Breaking the symmetry of the parametrically excited pendulum
• Simultaneous resonances in non-linear structural vibrations under two-frequency excitation
• Rotating solutions of the parametrically excited pendulum
• ZONES OF CHAOTIC BEHAVIOUR IN THE PARAMETRICALLY EXCITED PENDULUM
• A Quasiperiodic Mathieu–Hill Equation
• Transition Curves for the Quasi-Periodic Mathieu Equation
• Inverted oscillations of a driven pendulum
• Approximating the Escape Zone for the Parametrically Excited Pendulum
• On the parametric rolling of ships in a following sea under simultaneous nonlinear periodic surging
• Multiple-nodding oscillations of a driven inverted pendulum
• Dynamics of a Weakly Nonlinear System Subjected to Combined Parametric and External Excitation

This page was built for publication: Dynamics of a parametrically excited system with two forcing terms