Research On Fluid-structure Interaction Characteristics And Scale Effects Of Thin Plate Type Of Micro Cantilever

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.