Mechanical analysis of ultrasonic flow meter based on Doppler effect

This paper presents a study of the electrostatically actuated circular micro-plates used in MEMS ultrasonic flow meter. In this paper, a distributed model has been used to investigate the pull-in instability and frequency response of circular plate subjected to nonlinear distributed electrostatic force. A variational formulation based on Hamilton's principle is used to obtain the nonlinear governing equation of motion. The static and dynamic pull-in phenomena (parameters) limiting the stable regions of capacitive ultrasonic transducer determined for silicon and polysilicon diaphragms. The numerical results reveal that using polysilicon as structural layer leads to a decrease in the pull-in voltage and stable region in comparison with single crystal silicon. It has been shown that applying the bias DC voltage, beside the exciting AC voltage in transmitter part or beside periodic sound pressure waves in receiver part, decreases the stiffness of the system and so, causes a shift to the left in frequency response and increases the vibration amplitude. Thus, changing the bias DC voltage value can be used as a method for creating the tunable frequency structures, special in capacitive MEMS ultrasonic flow meters.