应用数学和力学2012，Vol.33Issue(11)：1284-1293,10.DOI:10.3879/j.issn.1000-0887.2012.11.004
非线性梁结构的参数振动稳定性及其主动控制
Parametric Vibration Stability and Active Control of Nonlinear Beams
摘要
Abstract
The vibration stability and active control of the parametricaily excited nonlinear beam structures were studied using the piezoelectric material. The velocity feedback control algorithm was applied to obtain the active damping. The cubic nonlinear equation of motion with damping was established by employing Hamilton' principle. The method of multiple scales was used to solve the equation of motion, and the stable region was obtained. The effects of the control gain and amplitude of the external force on the stable region and amplitude-frequency curve characteristics were analyzed numerically. From the numerical results it was seen that with the increase of the feedback control gain, the axial force to which the structure could be subjected increased, and in certain scope the structural active damping ratio also increased. With the increase of the control gain, the response amplitude decreases gradually, but the required control voltage exists peak value.关键词
梁/压电材料/参数振动/稳定性/主动控制/多尺度法Key words
beam/ piezoelectric material/ parametric vibration/ stability/ active control/ method of multiple scales分类
数理科学引用本文复制引用
李凤明,刘春川..非线性梁结构的参数振动稳定性及其主动控制[J].应用数学和力学,2012,33(11):1284-1293,10.基金项目
国家自然科学基金资助项目(11172084 （）
10672017 （）
50935002) （）
