Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). A Duffing oscillator is widely used as an archetypical model of mechanical resonators with nonlinear elastic behavior. In contrast, nonlinear dissipation effects in micromechanical oscillators are often overlooked. In this work, we consider a doubly clamped micromechanical beam oscillator, which exhibits nonlinearity in both elastic and dissipative properties. The dynamics of the oscillator is measured in both frequency and time domains and compared to theoretical predictions based on a Duffing-like model with nonlinear dissipation. We especially focus on the behavior of the system near bifurcation points. The results show that nonlinear dissipation can have a significant impact on the dynamics of micromechanical systems. To account for the results, we have developed a continuous model of a geometrically nonlinear beamstring with a linear Voigt-Kelvin viscoelastic constitutive law, which shows a relation between linear and nonlinear damping. However, the experimental results suggest that this model alone cannot fully account forall the experimentally observed nonlinear dissipation, and that additional nonlinear dissipative processes exist in our devices.

We experimentally study forced and self-excited oscillations of an optomechanical cavity, which is formed between a fiber Bragg grating that serves as a static mirror and a freely suspended metallic mechanical resonator that serves as a moving mirror. In the domain of small amplitude mechanical oscillations, we find that the optomechanical coupling is manifested as changes in the effective resonance frequency, damping rate, and cubic nonlinearity of the mechanical resonator. Moreover, self-excited oscillations of the micromechanical mirror are observed above a certain optical power threshold. A comparison between the experimental results and a theoretical model that we have recently derived and analyzed yields a good agreement. The comparison also indicates that the dominant optomechanical coupling mechanism is the heating of the metallic mirror due to optical absorption.

We study mechanical amplification and noise squeezing in a nonlinear nanomechanical resonator driven by an intense pump near its dynamical bifurcation point, namely, the onset of Duffing bistability. Phase sensitive amplification is achieved by a homodyne detection scheme, where the displacement detector's output, which has a correlated spectrum around the pump frequency, is down-converted by mixing with a local oscillator operating at the pump frequency with an adjustable phase. The down-converted signal at the mixer's output could be either amplified or deamplified, yielding noise squeezing, depending on the local oscillator phase.

We experimentally study stochastic resonance in a nonlinear bistable nanomechanical resonator. The device consists of a PdAu doubly clamped beam serving as a nanomechanical resonator excited capacitively by an adjacent gate electrode and its vibrations are detected optically. The resonator is tuned to its bistability region by an intense pump near a point of equal transition rates between its two metastable states. The pump is amplitude modulated, inducing modulation of the activation barrier between the states. When noise is added to the excitation, the resonator's displacement exhibits noise dependent amplification of the modulation signal. We measure the resonator's response in the time and frequency domains, the spectral amplification and the statistical distribution of the jump time.PACS numbers: 87.80.Mj 05.45.-a Stochastic resonance (SR) is a phenomenon in which an appropriate amount of noise is used to amplify a periodic signal acting on a bistable nonlinear system. 1−3SR has been demonstrated experimentally in electrical, optical, superconducting, and neuronal systems.4−10 SR could be used for amplification in nanomechanical devices in order to improve force detection sensitivity. 11−12Nanomechanical resonators operating in their nonlinear regime exhibit the well known Duffing bistability. In a Duffing oscillator 13 , above a critical excitation amplitude, the response becomes a multi-valued function of the frequency in some finite frequency range, and the system becomes bistable (with a low amplitude state S l and a high amplitude one S h ) with jump points in the frequency response. In the presence of noise, the oscillator can occasionally overcome the activation barrier and hop between the states.14 When an oscillator is excited in the bistability region near a point of equal transition rates between its states, an amplitude modulation (AM) of the force could be amplified by noise when the noise dependent transition rate is comparable to twice the modulation frequency. This type of SR, where the bistability property depends on the driving force, is usually referred to as high frequency SR. 12,15In this paper we demonstrate high frequency SR in our nanomechanical resonator and measure the noise dependent amplification. Our study extends previous work 11−12 by characterizing the SR by spectral amplification 19 , and by measuring the statistical distribution of the jump time at SR condition. The system under study consists of a nonlinear doubly clamped nanomechanical PdAu beam, excited capacitively by an adjacent gate electrode.16−17 The device is shown in the inset of Fig. 2. The bistability region of the device is found by exciting the resonator with a harmonic pump signal, sweeping its amplitude upward and then downward for constant pump frequency, calculating the difference between the two responses, and repeating for a range of frequencies. The result is shown in Fig. 1a. An example of a pump amplitude hysteresis loop for a constant pump frequency of 520.58kHz (the broken line in Fig. 1a) is shown ...

The nonlinear dynamical behavior of a micromechanical resonator acting as one of the mirrors in an optical resonance cavity is investigated. The mechanical motion is coupled to the optical power circulating inside the cavity both directly through the radiation pressure and indirectly through heating that gives rise to a frequency shift in the mechanical resonance and to thermal deformation. The energy stored in the optical cavity is assumed to follow the mirror displacement without any lag. In contrast, a finite thermal relaxation rate introduces retardation effects into the mechanical equation of motion through temperature dependent terms. Using a combined harmonic balance and averaging technique, slow envelope evolution equations are derived. In the limit of small mechanical vibrations, the micromechanical system can be described as a nonlinear Duffing-like oscillator. Coupling to the optical cavity is shown to introduce corrections to the linear dissipation, the nonlinear dissipation and the nonlinear elastic constants of the micromechanical mirror. The magnitude and the sign of these corrections depend on the exact position of the mirror and on the optical power incident on the cavity. In particular, the effective linear dissipation can become negative, causing self-excited mechanical oscillations to occur as a result of either a subcritical or supercritical Hopf bifurcation. The full slow envelope evolution equations are used to derive the amplitudes and the corresponding oscillation frequencies of different limit cycles, and the bifurcation behavior is analyzed in detail. Finally, the theoretical results are compared to numerical simulations using realistic values of various physical parameters, showing a very good correspondence.