Band-type resonance: non-discrete energetically optimal resonant states

Arion Pons*, Tsevi Beatus*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Structural resonance involves the absorption of inertial loads by a tuned structural elasticity: a process playing a key role in a wide range of biological and technological systems, including many biological and bio-inspired locomotion systems. Conventional linear and nonlinear resonant states typically exist at specific discrete frequencies and specific symmetric waveforms. This discreteness can be an obstacle to resonant control modulation: deviating from these states, by modulating waveform asymmetry or drive frequency, generally leads to losses in system efficiency. Here, we demonstrate a new strategy for achieving these modulations at no loss of energetic efficiency. Leveraging fundamental advances in nonlinear dynamics, we characterise a new form of structural resonance: band-type resonance, describing a continuous band of energetically optimal resonant states existing around conventional discrete resonant states. These states are a counterexample to the common supposition that deviation from a linear (or nonlinear) resonant frequency necessarily involves a loss of efficiency. We demonstrate how band-type resonant states can be generated via a spectral shaping approach: with small modifications to the system kinematic and load waveforms, we construct sets of frequency- and asymmetry-modulated resonant states that show equal energetic optimality to their conventional discrete analogues. The existence of these non-discrete resonant states in a huge range of oscillators—linear and nonlinear, in many different physical contexts—is a new dynamical systems phenomenon. It has implications not only for biological and bio-inspired locomotion systems but for a constellation of forced oscillator systems across physics, engineering, and biology.

Original languageAmerican English
Pages (from-to)1161-1192
Number of pages32
JournalNonlinear Dynamics
Issue number2
StatePublished - Jan 2023

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature B.V.


  • Biomimetic propulsion
  • Energetic optimality
  • Energy resonance
  • Global resonance
  • Nonlinear mechanics
  • Structural resonance


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