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

doi:10.7652/xjtuxb201311011

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

更新时间：2025-07-09

- Resonant Frequency of the Rectangular Micro-Cantilever in Fluid-Structure Interaction
- Vol. 47, Issue 11, Pages: 60-64(2013)
- 作者机构：
  
  西安交通大学机械制造系统工程国家重点实验室,西安,710049
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201311011
  CLC： TP212
- Online First：10 November 2013，
  
  Published：2013
- 稿件说明：
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Resonant Frequency of the Rectangular Micro-Cantilever in Fluid-Structure Interaction[J]. 2013, 47(11): 60-64.
DOI：

Resonant Frequency of the Rectangular Micro-Cantilever in Fluid-Structure Interaction[J]. 2013, 47(11): 60-64. DOI： 10.7652/xjtuxb201311011.

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。

Abstract

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 micro-cantilever and the fluid density

which facilitates fluid density measurement and sensor miniaturization.

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references

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