Forced vibrations of a nonlinear oscillator with weak fractional damping

Forced Vibrations for a Nonlinear Wave Equation

Nonlinear damping in a micromechanical oscillator

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,...

Dynamics of the Helmholtz Oscillator with Fractional Order Damping

The dynamics of the nonlinear Helmholtz Oscillator with fractional order damping is studied in detail. The discretization of the differential equations according to the Grünwald-Letnikov fractional derivative definition in order to get numerical simulations is reported. Comparison between solutions obtained through a fourth-order Runge-Kutta method and the fractional damping system is commented...

Stability of a nonlinear oscillator with random damping

A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be predicted from the analysis of the moments of the linearized equation. In the case of a white noise, an exact formula for the Lyapunov exponent of the system is ...

Nonlinear Damping in Nanomechanical Beam Oscillator

We investigate the impact of nonlinear damping on the dynamics of a nanomechanical doubly clamped beam. The beam is driven into nonlinear regime and the response is measured by a displacement detector. For data analysis we introduce a nonlinear damping term to Duffing equation. The experiment shows conclusively that accounting for nonlinear damping effects is needed for correct modeling of the ...