【作者】 赵亮；

【导师】 赵学增； 王飞；

【作者基本信息】 哈尔滨工业大学 ， 机械电子工程， 2019， 博士

【摘要】 随着微机电系统（MEMS）加工技术的发展,使得高精度微悬臂梁的设计与制造得以实现。基于微悬臂梁传感器的超微目标探测技术可以满足微纳米生物学、医学、化学和物理学等学科对微尺度下生物质、气体、粒子含量检测的多数需求,因而受到了学术界的广泛关注。采用微悬臂梁超微目标探测研究中的多数力学问题,又可以归结为微悬臂梁表面附着目标的识别问题。目前,对于这一问题的研究主要集中于一维微悬臂梁表面附着单集中粒子或表面附着均匀粒子层的质量识别,而实际应用中需充分考虑微悬臂梁本体的二维化且能够对附着物的质量和位置进行双参数识别,然而该方面内容研究目前相对匮乏。因此本课题以矩形薄板微悬臂梁表面附着超微粒子为研究对象,建立单微悬臂梁表面附着多目标的质量和位置与其动力学响应之间的关系模型,分析附着粒子对微悬臂梁谐振频率的影响,模型中充分考虑微悬臂梁二维化、尺寸效应的影响。通过有限元软件仿真和原子力显微镜实验测量两种方法,分别获得微悬臂梁附着粒子前后谐振频率的变化,并将获得的频率变化值作为已知量输入所建立的模型中,实现目标物质量和位置的双识别。针对表面附着有多个均匀粒子带的矩形薄板微悬臂梁动力学特性进行研究。分析均匀带状粘附粒子的分布特性,利用粒子间的van der Waals势能来表示粘附带状粒子与基底间的相互作用能,同时结合微悬臂梁弹性应变能以及动能,得出表面附着有多个均匀粒子带的薄板型微悬臂梁的能量模型。利用分析力学中的能量法对模型求解,首先采用振型叠加法对微悬臂梁真实振型进行近似,进而得到能量表达式的离散形式,利用拉格朗日方程建立微悬臂梁振动方程,对其进行求解获得谐振频率。分析不同因素对微悬臂梁谐振频率的影响,着重讨论粘附密度、粘附带数量以及周期分布粘附带占空比三个重要因素对谐振频率的影响规律。针对表面附着有多个集中质量体的薄板型微悬臂梁的动力学特性进行研究,分别使用经典理论（不考虑尺寸效应）和修正Cosserat理论（考虑尺寸效应）,利用一维欧拉伯努利梁特征函数组合假设二维薄板型微悬臂梁振型,并对能量方程进行矩阵化表示,由拉格朗日方程建立粘附有集中质量体的薄板型微悬臂梁的动力学模型,并与已发表论文数据进行对比验证模型的有效性。计算了粘附集中质量体的薄板型微悬臂梁的各阶弯曲谐振频率,给出了集中质量数为1⁵时的算例。应用所建立的模型分析不同参数对微悬臂梁频率产生的影响,重点研究了附着粒子的质量和位置对微悬臂梁谐振频率的影响规律,最后分析了空气阻尼对微悬臂梁谐振频率的影响。以矩形薄板微悬臂梁表面附着单个集中粒子以及多个集中粒子逆问题求解为研究目标,即根据微悬臂梁的动力学响应求取附着在微悬臂梁表面集中粒子的质量和位置。采用瑞利-里兹法构建振型特征函数,并对比粒子附着前后微悬臂梁的谐振频率,进而建立微悬臂梁表面附着目标的质量和位置与其动力学响应关系的多目标识别模型,通过该模型推导出微悬臂梁附着超微粒子前后谐振频率的变化和超微粒子参数（质量、数量和位置）的关系表达式。采用有限元仿真实验计算了不少于附着粒子总数三倍的微悬臂梁各阶谐振频率变化量,并将频率结果带入所建立的关系模型,利用非线性最小二乘法数值优化方法,拟合出不同粒子的位置和质量,最终实现每个粒子的单体质量和位置双识别。分析了不同长宽比微悬臂梁、附着不同粒子的质量以及附着不同位置的粒子对识别模型的影响。采用FIB聚焦离子/电子双束显微电镜系统制备不同尺寸的微悬臂梁,并在其表面沉积不同质量和不同位置的铂粒子,通过AFM系统分步测量铂粒子沉积前后微悬臂梁各阶谐振频率,对测量的实验数据进行分析,研究沉积不同的粒子对微悬臂梁谐振频率的影响规律。将实验测量的频率值输入本文所建立的微悬臂梁表面附着质量和位置双识别模型中,借助最小二乘法进行拟合求解,并将拟合结果与实验中所沉积粒子的测量值进行比较,证明了理论模型的有效性。基于目前所选用的微悬臂梁（微米级）以及设备所能达到的测量精度,实现了附着粒子与微悬臂梁质量比为0.5%的粒子质量和位置识别,质量识别精度可以达到皮克(10^-12g)级。更多还原

【Abstract】 The development of micro-electro mechanical systems（MEMS）processing technology enable the design and manufacture standard of high precision micro cantilevers.The ultra-micro target detection technology based on micro cantilever which meet the micro-scale measure needs for biomass,gas and partcicle in the micro-nano biology,medicine,chemistry and physics filed.has received great attention in recent decades.Most of the mechanical problems in the study of micro-cantilever ultra-fine target detection can be attributed to the identification problem of micro-cantilever surface attachment targets.Up to now,the limitation in this field is restricted in one-dimensional micro cantilever on the quality detection of the adsorbed particles on the surface or the uniformly adsorbed particle layer on the surface.In practical applications,the two dimension of micro-beam body and the double parameter identification of the adsorption mass and the position should be fully investigated which was researched scarely.In this paper,the thin-plate micro cantilever surface adsorption ultra-micro mass is taken as the research object,and the quantitative relationship model between the multi-target mass and position parameters attached to the surface of the single micro cantilever and the dynamic response is also established here.The resonant frequency of the microcantilever after the adsorption of the particles is analyzed.The model fully considers the effects of two-dimensional micro cantilever,size effect and adsorption effect.Two methods were measured by finite element software simulation and atomic force microscopy.The resonance frequency of the microcantilever attached particles was obtained,and the obtained frequency change value was used as the model input by the known quantity to achieve the target mass and dual identification of the location.The dynamic characteristics of thin-plate micro cantilever with multiple uniform adsorption bands attached to the surface are studied.The adsorption properties of uniform band-like adhesion mass are fully investigated,and the interaction energy between the band-like particles and the substrate are analyzed.The elastic strain energy and kinetic energy of the beam are also analyzed,given the corresponding mathematical expressions,finally leading to the energy model.For the analysis of the resonance frequency,the approximate analysis of the thin plate mode is firstly carried out,then the energy expression is modified and optimized,and the frequency of the cantilever beam vibration equation is obtained by the Lagrangian equation to solve the equation.The influence of different factors on the resonance frequency is analyzed.The influence of three important factors of the adhesion density,the number of adhesive bands and the duty cycle of the adhesion band on the resonance frequency is discussed.The dynamic characteristics of thin-plate microcantilever with multiple concentrated mass bodies attached to the surface are studied by using classical theory（regardless of size effect）and modified Cosserat theory（considering size effect）separately.One-dimensional Euler Bernoulli function combination is used to assume the two-dimensional thin plate cantilever beam vibration mode.The Lagrange equation is used to establish the dynamic model of the plate-type micro cantilever with the concentrated mass adhered.The validity of the model is verified by comparing with the published data.The bending natural frequencies and modes of the thin-plate type micro cantilever with the concentrating mass are calculated,and the examples of the concentrated masses of 1⁵ are given.Applying the model established in this paper,the influence of different parameters on the micro cantilever frequency is analyzed.The influence of different adsorption masses and position on the resonant frequency of micro cantilever is particularly studied.Finally,the effect of air damping on resonant frequency of microcantilever beam is analyzed.The inverse problem of solving the single particle and multiple particles on the surface of the flat micro cantilever is the goal of the research.According to the problem that the quality and position of the multi-object attached to the surface of the micro cantilever are obtained according to the dynamic response of the micro cantilever,further details are given to solve and verify the target.A multi-objective identification model is established by using the Rayleigh-Ritz method to establish the relationship between the mass and position of the micro-cantilever surface attachment target and its dynamic response.The model is used to derive the change of the resonant frequency before and after the attachment of the micro-beam and the quality of the mass（quality,The number and position）relationship.The finite element software was used to calculate the resonant frequencies of the micro cantilever beams obtained by particle loading before and after are taken as virtual measurement data.The quality and position of the loaded particles are detected according to the recognition algorithm.The results show that the calculated values are in agreement with the theoretical values,which means the correctness of method is verified.Through simulation analysis and theoretical calculation,the effects of different aspect ratio micro cantilever beams,particles with different adsorption masses and particles with different adsorption positions on the recognition model are analyzed.The FIB focused ion/electron double-beam micro-electron microscopy system was used to prepare micro-cantilever beams with different parameters and platinum particles of different masses and positions were deposited on the surface.The AFM system was used to measure the resonance of the micro-cantilever beam before and after deposition of platinum particles.Based on the experimentally measured frequency values and by use of the double-identification model of the surface quality and position of the micro cantilever beam established in this paper together with the least squares method,the obtained particle parameters are compared with the experimental values to prove the effectiveness of the theoretical model.The experimental data of the measurement is studied,and the influence of different parameters in practical application on the resonance frequency of the micro cantilever is analyzed,and the accuracy of the simulation analysis results is verified.Based on the currently selected microcantilever beam（micron level）and the measurement accuracy that can be achieved in the present device,particle mass and position recognition of the attached particle and microcantilever mass ratio of 0.5%are achieved,and the quality recognition accuracy can reach Pique(10^-12g)level.更多还原