Self-sustained oscillations with delayed velocity feedback


  • Damián H. Zanette Centro Atómico Bariloche



Nonlinear oscillator, Self-sustained oscillation, Oscillation suppression, Micromechanical devices


We study a model for a nonlinear mechanical oscillator, relevant to the dynamics of micro- and nanomechanical time-keeping devices, where periodic motion is sustained by a feedback force proportional to the oscillation velocity.  Specifically, we focus our attention on the effect of a time delay in the feedback loop, assumed to originate in the electric circuit that creates and injects the self-sustaining force. Stationary oscillating solutions to the equation of motion, whose stability is insured by the crucial role of nonlinearity,  are analytically obtained through suitable approximations. We show that a delay within the order of the oscillation period can suppress self-sustained oscillations. Numerical solutions are used to validate the analytical approximations.

Received: 6 February 2017,  Accepted: 8 March 2017; Edited by: A. Martí; Reviewed by: C. Masoller, Universitat Politécnica de Catalunya, Barcelona, Spain; DOI:

Cite as: D. H. Zanette, Papers in Physics 9, 090003 (2017)

This paper, by D. H. Zanette, is licensed under the Creative Commons Attribution License 3.0.



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How to Cite

Zanette, D. H. (2017). Self-sustained oscillations with delayed velocity feedback. Papers in Physics, 9, 090003.