  Nonlinear elastic effects play an important role in the dynamics of
microelectromechanical systems (MEMS). 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 frequency domain and
time domain and compared to theoretical predictions based on 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 nonlinear viscoelastic
string with Voigt-Kelvin dissipation relation, which shows a relation between
linear and nonlinear damping. However, the experimental results suggest that
this model alone cannot fully account for all the experimentally observed
nonlinear dissipation, and that additional nonlinear dissipative processes
exist in our devices.
