The ‘Indian rope trick’ for a parametrically excited flexible rod: linearized analysis

DOI10.1098/RSPA.2000.0530zbMath0974.74029OpenAlexW2046728141MaRDI QIDQ4946523

Alan R. Champneys, W. Barrie Fraser

Publication date: 28 August 2000

Published in: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2000.0530

zbMATH Keywords

parametric excitationFloquet theoryinverted pendulumvertical vibrationcritical rod lengthlinear non-autonomous inhomogeneous differential equationlinearly elastic stiff rodtorsion-free problemtwo-timing asymptotics

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics (74H10) Vibrations in dynamical problems in solid mechanics (74H45) Stability of dynamical problems in solid mechanics (74H55)

Related Items (4)

Application of the method of direct separation of motions to the parametric stabilization of an elastic wire ⋮ On the effect of damping on the stabilization of mechanical systems via parametric excitation ⋮ Excitation-Induced Stability and Phase Transition: A Review ⋮ Stabilization via parametric excitation of multi-dof statically unstable systems

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