矩形微悬臂梁的流固耦合谐振频率分析  

Resonant Frequency of the Rectangular Micro-Cantilever in Fluid-Structure Interaction

作　　者：赵立波[1] 徐龙起[1] 热合曼艾比布力 张桂铭[1] 王鸿雁 秦宇 刘志刚[4] 赵玉龙[1] 蒋庄德[1] 

机构地区：[1]西安交通大学机械制造系统工程国家重点实验室,西安710049 [2]新疆交通职业技术学院汽车与机电工程学院,乌鲁木齐831401 [3]陕西省计量科学研究院,西安710065 [4]西安交通大学热流科学与工程教育部重点实验室,西安710049

出　　处：《西安交通大学学报》2013年第11期60-64,共5页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(51375378;50836004;90923001);中央高校基本科研业务费专项资金资助项目(2012jdgz08);国家工信部科技重大专项项目(2011ZX04004-061);教育部长江学者和创新团队发展计划资助项目(IRT1033);教育部科学研究重大项目(311001);高等学校学科创新引智计划项目(B12016);陕西省科学技术研究发展计划项目(2012KJXX-01)

摘　　要：为了得到矩形微悬臂梁的谐振频率与流体密度的理论关系式,建立了微悬臂梁与流体的耦合振动微分方程.通过叠加微悬臂梁的真空振型替代微悬臂梁的流固耦合振型,将流体对微悬臂梁的影响转换为流体动压力,利用真空振型的正交性对振动微分方程进行求解,从而得到悬臂梁谐振频率与流体密度的函数关系.在此基础上,对浸没于10～30℃正庚烷和异辛烷中的单晶硅微悬臂梁的谐振频率进行理论计算、仿真分析和实验测量,将谐振频率的理论计算值分别与仿真和实验值进行比较,结果表明：理论值和仿真值的绝对偏差低于2.8％,理论值和实验值的绝对偏差低于0.9％,验证了悬臂梁的流固耦合谐振频率与流体密度理论关系式的正确性,为流体密度的测量和传感器尺寸的微型化提供了理论基础和参考依据.To obtain the theoretical relationship between the resonant frequency of a rectangular micro-cantilever and the fluid density,the differential equation of the micro-cantilever coupled with fluid is established through the method of vacuum mode superposition instead of the fluid-structure interaction mode to obtain the fluid hydrodynamic pressure instead of the effect of fluid on the micro-cantilever.Then the equation is solved to acquire the function of the resonant frequency and fluid density by making use of the vacuum mode orthogonality.The resonant frequencies of silicon micro-cantilever chip immersed in the n-heptane and isooctane at 10-30 ℃ are calculated and compared with simulation values and experimental measurements.The absolute deviations of the calculation values of the resonant frequency from the simulation and experimental values get less than 2.8％ and 0.9％,respectively.The theoretical formula can accurately describe the relationship between the resonant frequency of the rectangular microcantilever and the fluid density,which facilitates fluid density measurement and sensor miniaturization.

关 键 词：流固耦合 微悬臂梁 密度 谐振频率 

分 类 号：TP212[自动化与计算机技术—检测技术与自动化装置]