摘要
采用压电材料研究了参数激励非线性梁结构的运动稳定性及其主动控制,通过速度反馈控制算法获得主动阻尼,利用Hamilton原理建立含阻尼的立方非线性运动方程,采用多尺度方法求解运动方程获得稳定性区域.通过数值算例,分析了控制增益、外激振力幅值等因素对稳定性区域和幅频曲线特性的影响.分析表明:控制增益增大,结构所能承受的轴向力也增大,在一定范围内结构的主动阻尼比也增加;随着控制增益的增大,响应幅值逐渐降低,但所需的控制电压存在峰值点.
The vibration stability and active control of the parametrically excited nonlinear beam structures were studied using the piezoelectric material. The velocity feedback control al- gorithra 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 re- quired control voltage exists peak value.
出处
《应用数学和力学》
CSCD
北大核心
2012年第11期1284-1293,共10页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(11172084
10672017
50935002)
关键词
梁
压电材料
参数振动
稳定性
主动控制
多尺度法
beam
piezoelectric material
parametric vibration
stability
active control
meth-od of multiple scales