title: Transient and chaotic low-energy transfers in a system with bistable nonlinearity.
abstract: The low-energy dynamics of a two-dof system composed of a grounded linear oscillator coupled to a lightweight mass by means of a spring with both cubic nonlinear and negative linear components is investigated. The mechanisms leading to intense energy exchanges between the linear oscillator, excited by a low-energy impulse, and the nonlinear attachment are addressed. For lightly damped systems, it is shown that two main mechanisms arise: Aperiodic alternating in-well and cross-well oscillations of the nonlinear attachment, and secondary nonlinear beats occurring once the dynamics evolves solely in-well. The description of the former dissipative phenomenon is provided in a two-dimensional projection of the phase space, where transitions between in-well and cross-well oscillations are associated with sequences of crossings across a pseudo-separatrix. Whereas the second mechanism is described in terms of secondary limiting phase trajectories of the nonlinear attachment under certain resonance conditions. The analytical treatment of the two aformentioned low-energy transfer mechanisms relies on the reduction of the nonlinear dynamics and consequent analysis of the reduced dynamics by asymptotic techniques. Direct numerical simulations fully validate our analytical predictions.
authors.affiliation: Department of Structural and Geotechnical Engineering, SAPIENZA University of Rome, Rome, Italy.
authors.forename: F
authors.initials: F
authors.lastname: Romeo
authors.affiliation: Institute of Chemical Physics, RAS, Moscow, Russia.
authors.forename: L I
authors.initials: LI
authors.lastname: Manevitch
authors.affiliation: College of Engineering, University of Illinois at Urbana-Champaign, Champaign, Illinois 61820, USA.
authors.forename: L A
authors.initials: LA
authors.lastname: Bergman
authors.affiliation: College of Engineering, University of Illinois at Urbana-Champaign, Champaign, Illinois 61820, USA.
authors.forename: A
authors.initials: A
authors.lastname: Vakakis