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, 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 for S. Zaitsev ( ) · O. Shtempluck · E. Buks Department of Electrical Engineering, Technion–Israel Institute of Technology, Haifa 32000, Israel e-mail: [email protected] O. Gottlieb Department of Mechanical Engineering, Technion–Israel Institute of Technology, Haifa 32000, Israel all the experimentally observed nonlinear dissipation, and that additional nonlinear dissipative processes exist in our devices.