薄板型微悬臂梁流固耦合特性及其尺度效应研究
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摘要
微悬臂梁传感器是探索微观世界的重要工具，被广泛应用于微观领域形貌探测和参数测量。由于频率参数容易获得，通过获取微悬臂梁传感器谐振频率变化，进而间接探测被测对象的动态测量方法成为研究热点。微悬臂梁传感器主要工作于流体环境，而微悬臂梁传感器在流体中振动时产生的流固耦合现象将引起谐振频率异常下降，并表现出尺度效应，给以微悬臂梁传感器为工具的定量研究带来较大困难。因此揭示微悬臂梁传感器流固耦合特性及尺度效应影响机理，修正谐振频率与被测量之间的关系模型已成为一项重要的研究内容。
本文以确定微悬臂梁传感器谐振频率与流体密度、粘度和微悬臂梁材料特征长度等多参数之间的定量关系为目的，建立考虑尺度效应的二维微悬臂梁流固耦合模型，给出简化数值求解方法，在此基础之上，分析粘性流体环境下，微悬臂梁频率响应中的流固耦合特性，以及微尺度下表现出的尺度效应。
作为尺度效应中最为典型的类型之一，微尺度下，材料内部微结构非均匀性引起的尺寸效应将不能忽略。基于修正Cosserat理论建立了考虑尺寸效应的微平板二维力学模型，利用微分求积法(DQM)对微分方程进行了数值求解，分析了不同边界条件下，微平板力学特性中的尺寸效应。在尺寸效应的影响下，微平板静态挠度将减小而谐振频率将增大，并且随着板厚度及泊松比的增大，尺寸效应的影响逐渐减弱，而板长宽比的变化则与尺寸效应没有直接的关系。
流体环境下流固耦合作用将引起微结构的动力学特性发生变化。为获得更为准确的频率响应特性，建立了微平板振动边界与密闭腔内粘性流体发生耦合作用时，考虑尺寸效应及耦合面边界滑移这两种类型尺度效应的二维流固耦合模型，提出基于等效参数提取的简化数值求解方法，分析粘性流体环境下，不同边界微平板的频率响应特性。在流固耦合作用影响下，微平板各阶谐振频率及振幅均显著降低，且影响程度不但取决于流体的密度，还与粘度，雷诺数等参数密切相关。当考虑尺寸效应影响时，谐振频率受粘性流体影响的程度将减弱；而当引入边界滑移条件后，流固耦合作用对频率响应的影响同样有所降低，但是非常微弱。
以边界与粘性流体发生耦合作用微平板流固耦合特性研究为基础，建立浸于无限大粘性流体中的考虑尺度效应的微悬臂梁二维流固耦合方程组，分析微悬臂梁频率响应中的流固耦合特性。微尺度下，粘性流体对微悬臂梁的作用不再只是流体附连水质量，流体粘性力作用同样不能忽略。随着模态数的增加，同种粘性流体对谐振频率的影响也随之增大。同时随着微悬臂梁厚度的减小、泊松比的提高以及长宽比的增大，流固耦合作用的影响程度将逐渐增强。
针对薄板型微悬臂梁频率响应中的尺寸效应以及浸于粘性流体中的微悬臂梁流固耦合特性进行实验研究，基于测量结果对微悬臂梁谐振频率与尺寸效应、流固耦合特性之间的关系进行分析，论证了本文建立的理论模型和提出的基于等效参数提取的简化数值方法在处理薄板型微悬臂梁流固耦合特性问题上的有效性，同时证明了仿真结论的正确性。
本文通过对薄板型微悬臂梁流固耦合特性及尺度效应的研究，建立了谐振频率与流体密度、粘度和微悬臂梁材料特征长度等多因素之间的定量关系模型，分析了流固耦合作用及尺度效应影响下，微悬臂梁频率响应的变化规律，这对揭示流体对微纳米结构动力学特性影响及其表现出的尺度效应的物理机制、高灵敏微悬臂梁传感器设计和应用具有重要意义。
The microcantilever sensor is an important tool to explore the microscopic world,and it is widely used in the microscopic field for morphology detection and parametermeasurement. Since frequency parameters are easy to obtain, the dynamic measuringmethod which the object is indirectly detected through variation of resonancefrequencies of microcantilever sensors, has become a research hotspot. Most ofmicrocantilever sensors work in a fluid environment. The fluid-structure interactionphenomena caused by the microcantilever vibration in the fluid will cause abnormaldecline of resonant frequencies, and the scale effect occurs. This phenomenon hasbrought greater difficulties in quantitative research using the microcantilever sensor asa tool. Therefore, revealing mechanisms of fluid-structure interaction and scale effectfor microcantilever sensors, and then revising the relationship model between resonantfrequencies and the object measured，has become an important research content.
This paper aims at determining the multi-factor quantitative relationships betweenresonant frequencies of the microcantilever and the fluid density, viscosity,characteristic length of the material, and establishes a two-dimensional fluid-structureinteraction model which takes the scale effect into account for microcantilevers, andgives a simplify numerical method. On that basis, the fluid-structure interactioncharacteristics and the scale effect on the frequency response of microcantilevers areanalyzed in viscous fluid environment.
In micro scale, the size effect caused by the non-uniformity of materials internalmicrostructure can’t be neglected. Based on modified Cosserat theory and consideringthe size effect, this paper establishes a two-dimensional mechanical model of a microplate, provides the numerical solution of differential equations using differentialquadrature method (DQM), and analyses the size effect in mechanical properties of themicro plate under different boundary conditions. With the influence of size effect, theStatic bending deflection will decrease and the resonant frequency will increase. Withthe increase of thickness and Poisson's ratios of micro plate, the influence of the sizeeffect becomes weaker gradually. There is no direct relationship between the length-width ratios and the size effect.
The fluid-structure interaction causes dynamics variation of micro-structure influid environment. In order to obtain more accurate frequency response characteristics,this paper establishes a two-dimensional fluid-structure interaction model whichconsiders the size effect and the boundary slip when the micro plate boundary coupleswith the viscous fluid in closed cavity, proposes a simplified numerical method basedon equivalent parameters extracted, and analyses the frequency response of the micro plate under different boundary conditions in different viscous fluids. With theinfluence of the fluid-structure interaction effect, any order of resonant frequency andamplitude of the micro plate significantly decrease. The extent of the influence notonly depends on the density of the fluid, but also closely relates to the viscosity, theReynolds number and other parameters. When the size effect is considered, the viscousfluid will reduce the influence on the resonant frequency. When the boundary slipcondition is introduced, the fluid-structure interaction will reduce the influence on theresonant frequency, but very slightly.
Based on the research of fluid-structure interaction characteristics of microplatecoupled with the infinite viscous fluid, the paper establishes two-dimensional fluid-structure interaction equations considering the scale effect of the microcantileverimmersed in a viscous fluid, and analyzes the fluid-structure interaction characteristicsfor frequency response of the microcantilever. In micro scale, the fluid force on themicrocantilever is no longer just additional water mass, and the fluid viscous forcecan’t be neglected ether. With the increase of modal number, the viscous fluidinfluence on resonant frequency increases. Meanwhile, with the decrease of themicrocantilever thickness and the increases of Poisson's ratios and length-width ratios,the extent of the influence of the fluid-structure interaction will increase gradually.
Experimental study is carried out for the size effect of microcantilever immersedin air and for the fluid-structure interaction characteristics of microcantileverimmersed in a viscous fluid. Based on the measurement results, the relationshipbetween microcantilever resonant frequencies and the size effect, fluid-structureinteraction is analyzed. The effectiveness of the theoretical model established and thesimplified numerical method proposed based on the equivalent parameters extracted inthe processing of fluid-structure interaction characteristics and scale effect for sheet-type microcantilever is demonstrated, and the validation of the simulation conclusionsis proved.
This paper investigates the fluid-structure interaction and the scale effect,establishes multi-factor quantitative relationship between the resonant frequencies ofthe microcantilever and fluid density, viscosity, material characteristic length, andanalyses the variation of the frequency response of the microcantilever under theinfluence of the fluid-structure interaction and the scale effect. It is significantlyimportant to reveal the physical mechanism of the fluid and the scale effect on thedynamics of micro structures for the design and application of highly sensitivemicrocantilever sensors.
本文以确定微悬臂梁传感器谐振频率与流体密度、粘度和微悬臂梁材料特征长度等多参数之间的定量关系为目的，建立考虑尺度效应的二维微悬臂梁流固耦合模型，给出简化数值求解方法，在此基础之上，分析粘性流体环境下，微悬臂梁频率响应中的流固耦合特性，以及微尺度下表现出的尺度效应。
作为尺度效应中最为典型的类型之一，微尺度下，材料内部微结构非均匀性引起的尺寸效应将不能忽略。基于修正Cosserat理论建立了考虑尺寸效应的微平板二维力学模型，利用微分求积法(DQM)对微分方程进行了数值求解，分析了不同边界条件下，微平板力学特性中的尺寸效应。在尺寸效应的影响下，微平板静态挠度将减小而谐振频率将增大，并且随着板厚度及泊松比的增大，尺寸效应的影响逐渐减弱，而板长宽比的变化则与尺寸效应没有直接的关系。
流体环境下流固耦合作用将引起微结构的动力学特性发生变化。为获得更为准确的频率响应特性，建立了微平板振动边界与密闭腔内粘性流体发生耦合作用时，考虑尺寸效应及耦合面边界滑移这两种类型尺度效应的二维流固耦合模型，提出基于等效参数提取的简化数值求解方法，分析粘性流体环境下，不同边界微平板的频率响应特性。在流固耦合作用影响下，微平板各阶谐振频率及振幅均显著降低，且影响程度不但取决于流体的密度，还与粘度，雷诺数等参数密切相关。当考虑尺寸效应影响时，谐振频率受粘性流体影响的程度将减弱；而当引入边界滑移条件后，流固耦合作用对频率响应的影响同样有所降低，但是非常微弱。
以边界与粘性流体发生耦合作用微平板流固耦合特性研究为基础，建立浸于无限大粘性流体中的考虑尺度效应的微悬臂梁二维流固耦合方程组，分析微悬臂梁频率响应中的流固耦合特性。微尺度下，粘性流体对微悬臂梁的作用不再只是流体附连水质量，流体粘性力作用同样不能忽略。随着模态数的增加，同种粘性流体对谐振频率的影响也随之增大。同时随着微悬臂梁厚度的减小、泊松比的提高以及长宽比的增大，流固耦合作用的影响程度将逐渐增强。
针对薄板型微悬臂梁频率响应中的尺寸效应以及浸于粘性流体中的微悬臂梁流固耦合特性进行实验研究，基于测量结果对微悬臂梁谐振频率与尺寸效应、流固耦合特性之间的关系进行分析，论证了本文建立的理论模型和提出的基于等效参数提取的简化数值方法在处理薄板型微悬臂梁流固耦合特性问题上的有效性，同时证明了仿真结论的正确性。
本文通过对薄板型微悬臂梁流固耦合特性及尺度效应的研究，建立了谐振频率与流体密度、粘度和微悬臂梁材料特征长度等多因素之间的定量关系模型，分析了流固耦合作用及尺度效应影响下，微悬臂梁频率响应的变化规律，这对揭示流体对微纳米结构动力学特性影响及其表现出的尺度效应的物理机制、高灵敏微悬臂梁传感器设计和应用具有重要意义。
The microcantilever sensor is an important tool to explore the microscopic world,and it is widely used in the microscopic field for morphology detection and parametermeasurement. Since frequency parameters are easy to obtain, the dynamic measuringmethod which the object is indirectly detected through variation of resonancefrequencies of microcantilever sensors, has become a research hotspot. Most ofmicrocantilever sensors work in a fluid environment. The fluid-structure interactionphenomena caused by the microcantilever vibration in the fluid will cause abnormaldecline of resonant frequencies, and the scale effect occurs. This phenomenon hasbrought greater difficulties in quantitative research using the microcantilever sensor asa tool. Therefore, revealing mechanisms of fluid-structure interaction and scale effectfor microcantilever sensors, and then revising the relationship model between resonantfrequencies and the object measured，has become an important research content.
This paper aims at determining the multi-factor quantitative relationships betweenresonant frequencies of the microcantilever and the fluid density, viscosity,characteristic length of the material, and establishes a two-dimensional fluid-structureinteraction model which takes the scale effect into account for microcantilevers, andgives a simplify numerical method. On that basis, the fluid-structure interactioncharacteristics and the scale effect on the frequency response of microcantilevers areanalyzed in viscous fluid environment.
In micro scale, the size effect caused by the non-uniformity of materials internalmicrostructure can’t be neglected. Based on modified Cosserat theory and consideringthe size effect, this paper establishes a two-dimensional mechanical model of a microplate, provides the numerical solution of differential equations using differentialquadrature method (DQM), and analyses the size effect in mechanical properties of themicro plate under different boundary conditions. With the influence of size effect, theStatic bending deflection will decrease and the resonant frequency will increase. Withthe increase of thickness and Poisson's ratios of micro plate, the influence of the sizeeffect becomes weaker gradually. There is no direct relationship between the length-width ratios and the size effect.
The fluid-structure interaction causes dynamics variation of micro-structure influid environment. In order to obtain more accurate frequency response characteristics,this paper establishes a two-dimensional fluid-structure interaction model whichconsiders the size effect and the boundary slip when the micro plate boundary coupleswith the viscous fluid in closed cavity, proposes a simplified numerical method basedon equivalent parameters extracted, and analyses the frequency response of the micro plate under different boundary conditions in different viscous fluids. With theinfluence of the fluid-structure interaction effect, any order of resonant frequency andamplitude of the micro plate significantly decrease. The extent of the influence notonly depends on the density of the fluid, but also closely relates to the viscosity, theReynolds number and other parameters. When the size effect is considered, the viscousfluid will reduce the influence on the resonant frequency. When the boundary slipcondition is introduced, the fluid-structure interaction will reduce the influence on theresonant frequency, but very slightly.
Based on the research of fluid-structure interaction characteristics of microplatecoupled with the infinite viscous fluid, the paper establishes two-dimensional fluid-structure interaction equations considering the scale effect of the microcantileverimmersed in a viscous fluid, and analyzes the fluid-structure interaction characteristicsfor frequency response of the microcantilever. In micro scale, the fluid force on themicrocantilever is no longer just additional water mass, and the fluid viscous forcecan’t be neglected ether. With the increase of modal number, the viscous fluidinfluence on resonant frequency increases. Meanwhile, with the decrease of themicrocantilever thickness and the increases of Poisson's ratios and length-width ratios,the extent of the influence of the fluid-structure interaction will increase gradually.
Experimental study is carried out for the size effect of microcantilever immersedin air and for the fluid-structure interaction characteristics of microcantileverimmersed in a viscous fluid. Based on the measurement results, the relationshipbetween microcantilever resonant frequencies and the size effect, fluid-structureinteraction is analyzed. The effectiveness of the theoretical model established and thesimplified numerical method proposed based on the equivalent parameters extracted inthe processing of fluid-structure interaction characteristics and scale effect for sheet-type microcantilever is demonstrated, and the validation of the simulation conclusionsis proved.
This paper investigates the fluid-structure interaction and the scale effect,establishes multi-factor quantitative relationship between the resonant frequencies ofthe microcantilever and fluid density, viscosity, material characteristic length, andanalyses the variation of the frequency response of the microcantilever under theinfluence of the fluid-structure interaction and the scale effect. It is significantlyimportant to reveal the physical mechanism of the fluid and the scale effect on thedynamics of micro structures for the design and application of highly sensitivemicrocantilever sensors.
引文
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