Automatic locking of a parametrically resonating, base-excited, nonlinear beam

Nir Ben Shaya, Izhak Bucher, Amit Dolev

Research output: Contribution to journalArticlepeer-review


Described is a closed-loop control scheme capable of stabilizing a parametrically excited nonlinear structure in several vibration modes. By setting the relative phase between the spatially filtered response and the excitation, the open-loop unstable solution branches are stabilized under a 2:1 parametric excitation of a chosen mode of vibration. For a given phase, the closed-loop automatically locks on a limit cycle, through an Autoresonance scheme, at any desired point on the solution branches. Axially driven slender beams and nanowires develop large transverse vibration under suitable amplitudes and frequency base-excitation that are sensitive to small potential coupled field. To utilize such a structure as a sensor, stable and robust operation are made possible by the control scheme. In addition, an optimal operating point with large sensitivity to the sensed potential field can be set using phase as a tunable parameter. Detailed analysis of the dynamical behavior, experimental verifications, and demonstrations sheds light on some features of the system dynamics.

Original languageEnglish
Pages (from-to)1843-1867
Number of pages25
JournalNonlinear Dynamics
Issue number3
StatePublished - Nov 2021


  • Automatic resonance control
  • Nanowires sensors
  • Principal parametric resonance

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics


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