Internal resonance in a MEMS levitation force resonator

Abstract

In this work, we explore internal resonances in a levitation force microelectromechanical system-based actuator assuming flexible cantilever and clamped–clamped microbeam configurations. The levitation force is generated through a special arrangement of two-side stationary charged substrates and a central grounded stationary strip. The design assumes as well an upper flexible microbeam strip. The DC part of the excitation voltage pushes up the moving microbeam away from its lower stationary electrode. A superimposed harmonic AC voltage lets the flexible strip vibrate around its equilibrium position. Energy exchange among the computed lower vibration frequencies and their respective frequency and force response curves are explored for possibilities of principal parametric and internal resonances interactions. The generated responses are computed using the bifurcation toolbox MatCont. The effect of Von Karman nonlinearity to power the energy exchange within vibration modes is explored and dominant factors in the MEMS design for resonances are found from a two-parameter bifurcation analysis. Our results allow optimizing the micro-actuator device performance for future applications.