Dynamic stability of parametrically-excited linear resonant beams under periodic axial force  

作　　者：李晶 樊尚春 李艳 郭占社 

机构地区：[1]School of Instrument Science&Opto-electronics Engineering,Beihang University [2]Key Laboratory of Precision Opto-mechatronics Techonology,Ministry of Education [3]Key Laboratory of Inertial Science and Technology for National Defence [4]School of Information and Communication Engineering,North University of China

出　　处：《Chinese Physics B》2012年第11期94-101,共8页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant No. 60927005);the 2012 Innovation Foundation of BUAA for PhD Graduates;the Fundamental Research Funds for the Central Universities,China (Grant No. YWF-10-01-A17)

摘　　要：The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing equations of motion are derived by using the Rayleigh-Ritz method and transformed into Mathieu equations, which are formed to determine the stability criterion and stability regions for parametricallyexcited linear resonant beams. An improved stability criterion is obtained using periodic Lyapunov functions. The boundary points on the stable regions are determined by using a small parameter perturbation method. Numerical results and discussion are presented to highlight the effects of beam length, axial force and damped coefficient on the stability criterion and stability regions. While some stability rules are easy to anticipate, we draw some conclusions： with the increase of damped coefficient, stable regions arise; with the decrease of beam length, the conditions of the damped coefficient arise instead. These conclusions can provide a reference for the robust design of parametricallyexcited linear resonant sensors.The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing equations of motion are derived by using the Rayleigh-Ritz method and transformed into Mathieu equations, which are formed to determine the stability criterion and stability regions for parametricallyexcited linear resonant beams. An improved stability criterion is obtained using periodic Lyapunov functions. The boundary points on the stable regions are determined by using a small parameter perturbation method. Numerical results and discussion are presented to highlight the effects of beam length, axial force and damped coefficient on the stability criterion and stability regions. While some stability rules are easy to anticipate, we draw some conclusions： with the increase of damped coefficient, stable regions arise; with the decrease of beam length, the conditions of the damped coefficient arise instead. These conclusions can provide a reference for the robust design of parametricallyexcited linear resonant sensors.

关 键 词：resonant beams dynamic stability parametrically excitation periodic axial force 

分 类 号：TP212[自动化与计算机技术—检测技术与自动化装置] TH311[自动化与计算机技术—控制科学与工程]