Nonlinear Dynamics

, Volume 92, Issue 3, pp 1045–1059 | Cite as

Efficient potential well escape for bi-stable Duffing oscillators

  • Janav P. Udani
  • Andres F. Arrieta
Original Paper


The problem of escape from a potential well of bi-stable oscillators has attracted attention given the diversity of physical and engineering systems described by this mathematical model. Most previous studies have considered quasi-static dynamics leading to escape. In devising efficient escape strategies for structures, transient conditions have not yet received adequate consideration. In this study, the intra-well nonlinear resonant dynamics of bi-stable systems are studied and exploited, yielding a time-efficient strategy for triggering minimal amplitude escape by employing transient perturbations. The response characteristics of both, the symmetric and asymmetric double-well Duffing oscillators are explored analytically to identify the stable solution branches for any given forcing configuration. Based on the basins of attraction of the stable attractors, a novel actuation methodology employing controlled perturbations in the phase of the forcing for driving the system into a series of high-amplitude limit cycle oscillations and eventual escape to the desired stable solution is proposed. Additionally, accelerated settling to the desired configuration is achieved by implementing state feedback techniques. The proposed algorithm serves as a potential tool for implementing fast shape adaptation in bi-stable structural systems.


Bi-stable systems Duffing oscillator Nonlinear dynamics Escape Limit cycle oscillations 



J. P. Udani and A. F. Arrieta gratefully acknowledge the support of the Purdue Research Foundation (PRF); this research was funded through start-up funds provided by PRF.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringPurdue UniversityINUSA

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