高斯白噪声激励下微悬臂梁的瞬态均方响应研究

Transient Mean Square Response of a Microcantilever Beam Excited by Gaussian White Noise

采用集总参数建模方法,将微悬臂梁系统等效为弹簧质量阻尼系统。应用极点留数法,推导出MEMS中微悬臂梁在高斯白噪声随机激励下的瞬态均方响应的封闭解。结果表明极点留数法不仅比时域法和频域法更有效,而且避免了在时域计算积分的繁琐过程。最后讨论了阻尼比及噪声强度对系统瞬态均方响应的影响规律。

In this paper,the microcantilever beam system is equivalent to the spring mass damping system by lumped parameter modeling method.Then,the closed solution of the transient mean square response of the microcantilever beam under Gaussian white noise excitation is derived using pole residue method.The results show that the pole residue method is not only more efficient than the time domain method and the frequency domain method,but also avoids the tedious process of integrating in the time domain.Finally,the effects of damping ratio and noise intensity on the transient mean square response of the system are discussed.