Strong negative nonlinear friction from induced two-phonon processes in vibrational systems

Abstract

Self-sustained vibrations in systems ranging from lasers to clocks to biological systems are often associated with the coefficient of linear friction, which relates the friction force to the velocity, becoming negative. The runaway of the vibration amplitude is prevented by positive nonlinear friction that increases rapidly with the amplitude. Here we use a modulated electromechanical resonator to show that nonlinear friction can be made negative and sufficiently strong to overcome positive linear friction at large vibration amplitudes. The experiment involves applying a drive that simultaneously excites two phonons of the studied mode and a phonon of a faster decaying high-frequency mode. We study generic features of the oscillator dynamics with negative nonlinear friction. Remarkably, self-sustained vibrations of the oscillator require activation in this case. When, in addition, a resonant force is applied, a branch of large-amplitude forced vibrations can emerge, isolated from the branch of the ordinary small-amplitude response.

Frequency stabilization and noise-induced spectral narrowing in resonators with zero dispersion

“…The zero dispersion in our resonator is obtained by tuning the negative electrostatic nonlinearity relative to the positive intrinsic nonlinearity of the springs. Non-monotonicity of a transformed backbone line can also be achieved using other methods, such as the coupling of two nanomechanical resonators 51 or the negative nonlinear friction induced by dynamical backaction from a photon or phonon cavity 52 . Thus, zero dispersion is a rather generic feature of mechanical resonators and such resonators provide a well-controlled platform to investigate and exploit zero-dispersion phenomena reported in the present work as well as others that have not yet been experimentally observed.…”

The effects of nonlinear damping on degenerate parametric amplification

“…We include nonlinear damping in the model for three important reasons: (1) it is commonly observed in experiments across many fields [57][58][59][60][61][62][63][64][65][66][67][68][69], (2) it arises from fundamental microscopic considerations in micro/nano-resonators [59,70], and (3) it allows for the closure of the nontrivial response branches in parametric resonance by saddle-node bifurcations that can occur even near resonance (in fact, it can limit the response even in the absence of the Duffing nonlinearity). In order to make the third point, consider an oscillator being excited only parametrically, in which case the parametric instability threshold can be observed from Eq.…”

“…In addition, nonlinear damping has been observed in macroscopic mechanical systems, such as large-amplitude ship rolling motions [64], concrete structures [65], stainless steel rectangular plates, stainless steel circular cylindrical panels, and zirconium alloy hollow rods [66]. Nonlinear damping of a given mode can also result from mode interactions such as induced two-phonon processes [67] and internal resonances [59,68,69]. In addition to the experimental observations, many theoretical works have also been completed, covering the topics of the relaxation of nonlinear oscillators interacting with a medium [70], estimation using Melnikov theory [71], estimation using analytic wavelet transform [72], dynamic response to harmonic drive [62], and characterization using the ringdown response [63].…”

Phase Control of Self-Excited Parametric Resonators

“…The device immediately drops off the stable parametric resonance branch or the amplitude grows rapidly until the device shorts to an electrode. Analogous behavior in the vicinity of η 0 should be obtainable for parametric resonators with stiffening nonlinearity and negative nonlinear damping [57,78].…”