Nonlinear interactions between vibration modes with vastly different eigenfrequencies

Abstract Nonlinear interactions between modes with eigenfrequencies that differ by orders of magnitude are ubiquitous in various fields of physics, ranging from cavity optomechanics to aeroelastic systems. Simplifying their description to a minimal model and grasping the essential physics is typically a system-specific challenge. We show that the complex dynamics of these interactions can be distilled into a single generic form, namely, the Stuart-Landau oscillator. With our model, we study the injection locking and frequency pulling of a low-frequency mode interacting with a blue-detuned high-frequency mode, which generate frequency combs. Such combs are tunable around both the high and low carrier frequencies. By discussing the analogy with a simple mechanical system model, we offer a minimalistic conceptual view of these complex interactions originating the frequency combs, together with showcasing their frequency tunability

Amplitude stabilization in a synchronized nonlinear nanomechanical oscillator

International audienceIn contrast to the well-known phenomenon of frequency stabilization in a synchronized noisy nonlinear oscillator, little is known about its amplitude stability. In this paper, we investigate experimentally and theoretically the amplitude evolution and stability of a nonlinear nanomechanical self-sustained oscillator that is synchronized with an external harmonic drive. We show that the phase difference between the tones plays a critical role on the amplitude level, and we demonstrate that in the strongly nonlinear regime, its amplitude fluctuations are reduced considerably. These findings bring to light a new facet of the synchronization phenomenon, extending its range of applications beyond the field of clock-references and suggesting a new means to enhance oscillator amplitude stability.</p

Amplitude stabilization in a synchronized nonlinear nanomechanical oscillator

International audienceIn contrast to the well-known phenomenon of frequency stabilization in a synchronized noisy nonlinear oscillator, little is known about its amplitude stability. In this paper, we investigate experimentally and theoretically the amplitude evolution and stability of a nonlinear nanomechanical self-sustained oscillator that is synchronized with an external harmonic drive. We show that the phase difference between the tones plays a critical role on the amplitude level, and we demonstrate that in the strongly nonlinear regime, its amplitude fluctuations are reduced considerably. These findings bring to light a new facet of the synchronization phenomenon, extending its range of applications beyond the field of clock-references and suggesting a new means to enhance oscillator amplitude stability.</p

Amplitude stabilization in a synchronized nonlinear nanomechanical oscillator

International audienceIn contrast to the well-known phenomenon of frequency stabilization in a synchronized noisy nonlinear oscillator, little is known about its amplitude stability. In this paper, we investigate experimentally and theoretically the amplitude evolution and stability of a nonlinear nanomechanical self-sustained oscillator that is synchronized with an external harmonic drive. We show that the phase difference between the tones plays a critical role on the amplitude level, and we demonstrate that in the strongly nonlinear regime, its amplitude fluctuations are reduced considerably. These findings bring to light a new facet of the synchronization phenomenon, extending its range of applications beyond the field of clock-references and suggesting a new means to enhance oscillator amplitude stability.</p

Controllable branching of robust response patterns in nonlinear mechanical resonators

Feedback control applied to mechanical resonators can lead to the formation of various complex dynamic behaviors. Here the authors demonstrate flexible and controllable switching between dynamical structures in the response of harmonically driven micro-mechanical resonators

Tuning nonlinear damping in graphene nanoresonators by parametric–direct internal resonance

Mechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. To date, no experimental evidence of this enhancement has been realized. In this letter, we experimentally show that nanoresonators driven into parametric-direct internal resonance provide supporting evidence for the microscopic theory of nonlinear dissipation. By regulating the drive level, we tune the parametric resonance of a graphene nanodrum over a range of 40–70 MHz to reach successive two-to-one internal resonances, leading to a nearly two-fold increase of the nonlinear damping. Our study opens up a route towards utilizing modal interactions and parametric resonance to realize resonators with engineered nonlinear dissipation over wide frequency range.</p

Bifurcation Generated Mechanical Frequency Comb

We demonstrate a novel response of a nonlinear micromechanical resonator when operated in a region of strong, nonlinear mode coupling. The system is excited with a single drive signal and its response is characterized by periodic amplitude modulations that occur at timescales based on system parameters. The periodic amplitude modulations of the resonator are a consequence of nonlinear mode coupling and are responsible for the emergence of a "frequency-comb" regime in the spectral response. By considering a generic model for a 13 internal resonance, we demonstrate that the novel behavior results from a saddle node on an invariant circle (SNIC) bifurcation. The ability to control the operating parameters of the micromechanical structures reported here makes the simple micromechanical resonator an ideal test bed to study the dynamic response of SNIC behavior demonstrated in mechanical, optical, and biological systems