TY - GEN
T1 - Splitting of separatrices in the rapidly forced duffing oscillator
AU - Vakakis, Alexander F.
N1 - Publisher Copyright:
© 1993 American Society of Mechanical Engineers (ASME). All rights reserved.
PY - 1993
Y1 - 1993
N2 - The splitting of the stable and unstable manifolds of the rapidly forced Duffmg oscillator with negative stiffness is investigated. The method used relies on the computation of analytic approximations for the orbits on the perturbed manifolds, and the asymptotic approximation of these orbits by successive integrations by parts. It is shown, that the splitting of the manifolds becomes exponentially small as the perturbation parameter tends to zero, and that the estimate for the splitting distance given by the Melnikov Integral dominates over high order corrections.
AB - The splitting of the stable and unstable manifolds of the rapidly forced Duffmg oscillator with negative stiffness is investigated. The method used relies on the computation of analytic approximations for the orbits on the perturbed manifolds, and the asymptotic approximation of these orbits by successive integrations by parts. It is shown, that the splitting of the manifolds becomes exponentially small as the perturbation parameter tends to zero, and that the estimate for the splitting distance given by the Melnikov Integral dominates over high order corrections.
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U2 - 10.1115/detc1993-0051
DO - 10.1115/detc1993-0051
M3 - Conference contribution
AN - SCOPUS:85104188351
T3 - Proceedings of the ASME Design Engineering Technical Conference
SP - 249
EP - 255
BT - 14th Biennial Conference on Mechanical Vibration and Noise
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 1993 Design Technical Conferences, DETC 1993
Y2 - 19 September 1993 through 22 September 1993
ER -