基于Wavelet-Galerkin法的微机械谐振器件挤压膜阻尼求解方法研究  

A Method for Calculating Squeeze Film Damping of Micro-mechanical Resonator Device Based on Wavelet-Galerkin Method

作　　者：刘宗斌[1] 刘相法[2] 周勇[1] 

机构地区：[1]江苏省特种设备安全监督检验研究院无锡分院,无锡214000 [2]潍坊科技学院,潍坊262700

出　　处：《机械科学与技术》2012年第7期1156-1160,共5页Mechanical Science and Technology for Aerospace Engineering

摘　　要：利用Wavelet-Galerkin方法对求解微机械谐振器件的挤压膜阻尼进行计算。首先选定一个微谐振器件挤压膜阻尼的模型,并列出它的微分方程和边界条件,系统在设定一个已知输入的情况下,对系统的流体压力响应用Daubechies小波基进行展开,利用Galerkin法求解相应的展开系数,以得到方程的近似解。由于Daubechies小波不存在解析表达式且具有强烈的震荡性,因此在Galerkin法中需要涉及到的小波的求导和积分,即所谓的关联系数,本文中也做了相应计算。利用上述方法,对给定参数的模型进行分析计算,计算结果说明该方法子分析分析挤压膜阻尼方面是有效的。Correctly predicting the squeeze film damping is of utmost importance for designing a micro-electro-me- chanical system（MEMS）. We use the Wavelet-Galerkin method to calculate the squeeze film damping of its mico- mechanical resonator device. We set up its squeeze film damping model and work out its differential equations and boundary conditions. Then we carry out some necessary simplification of the equations. We use the Daubechies wavelet to expand the fluid pressure response of the MEMS, assuming that one input is known. Finally, we calcu- late the expansion coefficient with the Wavelet-Galerkin method so as to obtain the approximate solutions of the equations. In view of the fact that the Daubechies wavelet has no analytical expression and has strong oscillation, we also calculate the correlation coefficient, which is the derivation and integral of the wavelet involved in the Wavelet-Galerkin method. We use our method to calculate the model with given parameters and compare the calcu- lated results with those obtained with the traditional methods. The comparison results show that our method is effec- tive for analyzing squeeze film damping and has a simple calculation process and fast calculation sneed.

关 键 词：挤压膜阻尼 Wavelet-Galerkin 关联系数 DAUBECHIES小波 

分 类 号：TH113.1[机械工程—机械设计及理论]