Analysis And Control Of Micro-cantilever With Van Der Waals Forces

Micro electro mechanical system (MEMS) is a multi-discipline crossed and new subject arising in1980s. Micro-cantilever is a typical structure, and is frequently used in switches and sensors in MEMS. Its dynamic performance affects the functions of MEMS directly. At present Van der Waals force is neglected in most studies. However, Van der Waals force should not be ignored in the micro-nano scale.This paper focuses on the dynamics and control of micro-cantilever with Van der Waals forces, including the periodic solution, performance of dynamics and control of chaotic motion. The main work and results are the followings:1. Using lumped parameter method, the dynamic model for the micro-cantilever is established. Van der Waals force is taken into account based on the’mass-spring-damping’ model. The effects of Van der Waals forces on the two plates of the micro-cantilever are analyzed. With the energy method, an approximate analytic solution of dynamic equation is obtained. Comparing with the results from numerical method, named fourth-order Runge-Kutta method, the approximate analytic solution has higher accuracy in lower order sub-harmonic vibration although it has large errors in higher order sub-harmonic vibration. With the approximate analytic solution, it is convenient to find out how the variations of the parameters of system affect the dynamic performance of the system.2. The impacts of Van der Waals force on the pull-in voltage, the state of motion and the dynamic bifurcation are studied by changing the parameter which is an index of Van der Waals force. The results show that the pull-in voltage will increases with the increasing of the parameter within limits. The state of motion will be changed with the change of Van der Waals forces. And in some of range, the stable equilibrium position with no external incentive and the cycle central position with external incentive will be changed along with the change of the parameter. Also it is shown that Van der Waals force can make some changes of bifurcation points or cycle central position. It is to say that the bifurcation points and cycle central position of system will be changed with the increasing of the parameter.3. Using MATLAB to simulate the system, the edge of chaos with changing one parameter of system is found by approximate entropy. The approximate entropies undergo a change from zero into some positive numbers, or vice versa. Also the dynamic performance of system is analyzed at the edge of chaos. The results show that the chaotic motion coexists with the cyclic motion at the edge of chaos, and the edge of chaos is near to the bifurcation points. In addition to these, the controlling of chaos with both piecewise quadratic function method and coupled feedback method are realized with the control parameters obtained from the bifurcation diagram.