An investigation into the electrostatic force representation for electrically actuated microelectromechanical systems

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TECHNICAL PAPER

An investigation into the electrostatic force representation for electrically actuated microelectromechanical systems K. Larkin1 • J. Ceniceros1 • H. Abdelmoula1 • A. Abdelkefi1 Received: 20 March 2020 / Accepted: 3 April 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract The ever-increasing demand for microelectromechanical systems (MEMS) in modern electronics has reinforced the need for extremely accurate analytical and reduced-order models to aid in the design of MEMS devices. Many MEMS designs consist of cantilever beams with a tip mass attached at the free end to act as a courter electrode for electrical actuation. One critical modeling aspect of electrically actuated MEMS is the electrostatic force that drives these systems. The two most used representations in the literature approximate the electrostatic force between two electrodes as a point force. In this work, the effects of the representation of the electrostatic force for electrically actuated microelectromechanical systems are investigated. The system under investigation is composed of a beam with an electrode attached to its end. The distributed force, rigid body, and point mass electrostatic force representations are modeled, studied, and their output results are compared qualitatively. Static and frequency analyses are carried out to investigate the influences of the electrostatic force representation on the static pull-in, fundamental natural frequency, and mode shape of the system. A nonlinear distributed-parameter model is then developed in order to determine and characterize the response of electrically actuated systems when considering various representation of the electrostatic forces. The results show that the size of the electrode may strongly affect the natural frequencies and static pull-in when the point mass, rigid body, and plate representations are considered. From nonlinear analysis, it is also proven that the representation may affect the hardening behavior of the system and its dynamic pull-in. This modeling and analysis give guidelines about the usefulness of the electrostatic force representations and possible erroneous assumptions that can be made which may result in inaccurate design and optimal performance detection for electrostatically actuated systems.

1 Introduction A wide variety of microelectromechanical systems (MEMS) devices exists today including actuators, resonators, energy harvesters, and sensors. Many of these systems rely on electrostatic forcing for actuation or sensing purposes (Batra et al. 2007). MEMS actuators or switches (Toler et al. 2013) use an electrostatic force to rapidly open and close electronic circuit. MEMS resonators (Ilyas et al. 2019) rely on an electrostatic force for actuation purposes. Sensors, such as MEMS mass/chemical sensors, accelerometers, or gyroscopes rely on electrostatic actuation for sensing and/or actuation (Yazdi et al. 1998; Rasekh and Khadem 2013). Due to the variety of & A. Abdelkefi abdu@