Periodic and chaotic behaviour of the autonomous impact resonator

Abstract

This paper describes the resonance characteristics of the autonomous impact resonator, a self resonating silicon resonator consisting only of a capacitive microbridge, a resistor and a d.c.-source. Since the oscillation is based on large vibrational amplitudes and on non-linear effects, the autonomous impact oscillator exhibits periodic as well as chaotic behaviour. An electromechanical model and a general mathematical description is given. The model is experimentally verified and the results are compared with simulations. The experimental results address the influence of the d.c.-voltage, the effect of the charging and discharging resistors, the influence of air damping and of the parasitic capacitance.