Escape of a forced-damped particle from weakly nonlinear truncated potential well
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11071_2020_5987_ReferencePDF.pdf
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8304b493f7aa850a4f7316762c4434d4
Author(s)
Farid, M.
Gendelman, O. V
Date Issued
January 5, 2021
Publisher
Springer Netherlands
Version
Author's final manuscript
Abstract
Abstract
Escape from a potential well is an extreme example of transient behavior. We consider the escape of the harmonically forced particle under viscous damping from the benchmark truncated weakly nonlinear potential well. Main attention is paid to most interesting case of primary 1:1 resonance. The treatment is based on multiple-scales analysis and exploration of the slow-flow dynamics. Contrary to Hamiltonian case described in earlier works, in the case with damping the slow-flow equations is not integrable. However, if the damping is small enough, it is possible to analyze the perturbed slow-flow equations. The effect of the damping on the escape threshold is evaluated in an explicit analytic form. The substantial difference between the linear and weakly nonlinear cases in terms of the slow-flow dynamics of the escape mechanisms is demonstrated and discussed.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1007/s11071-020-05987-8
