Dynamics regularization with tree-like structures

• Author(s) / Creator(s)

  • Niewenhuis et al.

• The dynamics of a fully nonlinear, tree-structured resonator and its response
  to a broadband forcing of the branches is examined. It is shown that the
  broadband forcing yields a transfer of energy between the parts of the spectrum
  so that the spectrum becomes progressively more narrow-band for each level of
  the tree-like structure in the direction of the stem. We show that this behavior
  is in contrast to the response of a linear oscillator, which simply filters out the
  harmonics away from the resonance. We term such behaviour “regularization”
  and examine its significance for two- and three-dimensional motion using a
  Lagrangian framework. Key to our analysis is to investigate the dependence
  of the spectrum of motion, and its narrowing, on the parameters of the
  tree-like structure, for instance the lengths of different branches. Model
  predictions are obtained for idealized wind forcing characterized by an airflow
  that is interrupted at random time intervals. Our numerically-derived results
  are then compared against the data collected from select analogue laboratory
  experiments, which confirm the robust nature of the vibration regularization.

• Date created

  2018-10-23

• Subjects / Keywords

  • Nonlinear dynamics
  • Coupled nonlinear oscillators
  • Tree-like structures
  • Dynamics regularization

• Type of Item

  Article (Published)

• DOI

  https://doi.org/10.7939/R3RV0DG7X

• License

  Attribution-NonCommercial 4.0 International