Self-sustained oscillations with delayed velocity feedback

Abstract

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. Marti;  Reviewed by: C. Masoller, Universitat Politecnica de Catalunya, Barcelona, Spain;  DOI: http://dx.doi.org/10.4279/PIP.090003 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 .