Analysis Of Dynamic Characteristics Of Micro-Ring Under Non-Uniform Electric Field

Micro-Electro-Mechanical System(MEMS)is a mechatronic system with a feature size in the sub-micron or millimeter range.Electrostatic driving has been widely used in micro-electromechanical systems.At present,researches on electrostatically driven microstructures in microelectromechanical systems focus on simple structure,and there are few studies on ring structures.This paper establishes a mathematical model for the microelectrostatic motor in the micro-electro-mechanical system and studies the response and stability of the electrostatically driven micro-ring under dynamic voltage control and the dynamic characteristics of the rotating micro-ring under the action of a point electrostatic force.The main research work of this dissertation is as follows:(1)Based on the thin shell theory and the electrostatic force theory,a theoretical model of a static micro-ring under the action of the electrostatic force is established.And the dynamic equation of the rotating micro ring under the action of a point electrostatic force is established.(2)The Galerkin method is used to discretize the motion equation,and the discretized motion equation is used for modal analysis of the ring to obtain the natural frequency and mode shape of the micro ring.Considering that there is a certain amount of damping in the system,a damping term is added to the equation of motion.(3)The equation of motion is solved numerically by the Runge-Kutta method,and the response of the system is obtained.Floquet theory is used to analyze the stability of the system,and finally,the influence of voltage,excitation frequency,damping,electrode span and rotational angular velocity on the response and stability of the system is explored.(4)The dynamic equation of the rotating ring is used to solve the natural frequency of the rotating micro-ring system,and the influence of different parameters on the stiffness of the dynamic equation of the rotating micro-ring system under the action of a point electrostatic force is explored.In this study,the static micro-ring and rotating micro-ring under the electrostatic force are modeled and their motion equations are solved,and the influence of multiple parameters on the electrostatic-driven micro-ring system is analyzed.The simulation results show that:structural damping affects the stability of the system The unstable region is mostly near the fundamental frequency,frequency multiplication and frequency division.Voltage,electrode span and excitation frequency all have a great influence on the stability and response of the system;the rotation speed and voltage will affect the dynamic equation of the rotating micro-ring.The rotation speed and voltage have a great influence on the stiffness term in the dynamic equation of the rotating micro-ring,which has certain reference value for the design and manufacture of the micro-electrostatic motor.