Electrostatically Actuated BIO-MEMS Circular Membrane Resonator Sensors: Voltage Response of Primary Resonance

Abstract This paper deals with the voltage-amplitude relationship during the primary resonance of electrostatically actuated circular membrane resonator sensors within the context of BIO-MEMS. The motion of these membranes is governed by a partial differential equation, which is nondimensionalized for analysis. This equation incorporates both damping effects and soft electrostatic actuation. The actuation AC frequency is set close to half of the membrane’s first natural frequency, leading to primary resonance. To investigate membrane’s voltage response, two principal methods were employed: the method of multiple scales (MMS) and a reduced order model (ROM) that incorporates two modes of vibration. This research provides insights into how the circular membrane resonator sensors behave under varying actuation voltages and examines the effects of damping and frequency on the voltage response. It was predicted that an increase in damping or detuning of frequency increases the pull-in voltage.