Numerical Investigations of Parametrically Excited Non-linear Multi Degree of Freedom Micro-electromechanical Systems

More and more systems exploit parametric excitation (PE) to improve their performance compared to conventional system. Especially in the field of micro-electromechanical systems (MEMS) such technologies rapidly gain in importance. Different to conventional resonance cases PE may destabilise the system’s rest position when parametrically excited time-periodically with a certain PE frequency. At such parametric resonances vibrations are only limited due to non-linearities. The system is repelled by the unstable rest position and enters a bifurcated limit cycle. Finding these limit cycles has become more easy in recent years. Advances have been made in numerical path following tools regarding both their power and their user friendliness. As a result, designing such systems has become more common. Indeed, the focus of studies has been on 1DOF systems mostly. However, for multi degree of freedom systems choosing a meaningful phase space to discuss the results is a task on its own. Quasi-modally transforming the equations of motion, the vibrations are decomposed allowing one to focus on the predominant modes. By concentrating on these predominant modes, continuation results can be displayed in meaningfully reduced phase-parameter spaces. Basins of attraction can be found in Poincaré sections of these phase-parameter spaces. ∗Address all correspondence to this author. Employing these approaches, it is demonstrated how to investigate a non-linear 2DOF PE MEMS, how to change the characteristics of the limit cycles and how this affects their basins of