The theoretical static response of electrostatic fixed–fixed beam microactuators

• Published in: Smart materials and structures Vol. 17; no. 6; pp. 065017 - 065017 (9)
• Main Author: Lee, Ki Bang
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.12.2008; Institute of Physics
• Subjects: Applied sciences; Electronics; Exact sciences and technology; General equipment and techniques; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Microelectronic fabrication (materials and surfaces technology); Physics; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Transducers; Error estimation; Pull in voltage; Capacitive transducer; Measurement sensor; Microactuators; Electric motors; Exact solution; Galerkin-Petrov method; Electrostatic machine; Modelling; Non linear effect; Differential method; Electrostatic actuators; Microelectromechanical device
• ISSN: 0964-1726; 1361-665X
• DOI: 10.1088/0964-1726/17/6/065017

A closed-form solution for the static response of fixed -fixed beam actuators to an applied voltage has been successfully derived to understand the nonlinear behavior of the actuator and to provide a guideline for the actuator design. A cubic force balance equation is obtained by applying the Galerkin method to the differential equation for the fixed -fixed beam actuator under an electrostatic force. Afterward, the cubic equation is theoretically solved for the center deflection of the beam, the pull-in center deflection, and the pull-in voltage. The theoretical center deflection follows that from numerical analysis of the original force balance equation well, within an error of 2.3%. The closed-form pull-in voltage and center deflection are in good agreement with those of the numerical analysis within errors of 0.46% and 2.3%, respectively. The theoretical pull-in voltage is also compared to that of a previous work obtained with a numerical method. The developed theory as well as the derived solutions can be used to design microactuators and sensors based on electrostatic fixed -fixed beam actuators.