吸附引起的翘曲及其对微悬臂梁静态响应的影响  

Warping Caused by Adsorption and Its Effect on the Static Response of Microcantilevers

作　　者：王振兴 张能辉[1] WANG Zhenxing;ZHANG Nenghui(Shanghai Institute of Applied Mathematics and Mechanics,Shanghai Key Laboratory of Mechanics in Energy Engineering,School of Mechanics and Engineering Science,Shanghai University,Shanghai 200072,China)

机构地区：[1]上海大学力学与工程科学学院,上海市应用数学和力学研究所,上海市力学在能源工程中的应用重点实验室,上海200072

出　　处：《力学季刊》2025年第1期64-75,共12页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(12172204,11772182,11272193,10872121)。

摘　　要：为满足新的检测需求并实现高灵敏度,微梁生物传感器技术在信号解读模型的发展方面遭遇挑战.我们通过对表面吸附作用下微梁准静态检测信号的3D有限元模拟,揭示了微梁横截面翘曲的非对称分布特征,然而现有考虑剪切变形的理论模型无法描述这种非对称翘曲变形.针对这一问题,首先,将分子完全吸附简化为作用于微梁表面的均匀分布表面应力,通过3D有限元模拟获得翘曲零点分布规律.然后,利用平面弹性理论的半逆解法,在变形后的横截面上确定与非对称翘曲特征相适应的切应力分布和剪力,由此改进了Timoshenko梁理论,建立了预测微梁准静态检测信号的新模型.最后,通过比对实验结果和有限元模拟验证解析模型.结果表明,本文改进模型预测与有关微梁实验吻合良好,且在现有吸附-微梁静态实验所选用的几何尺寸范围内(长厚比200~500,长宽比3~7),本文改进模型关于微梁自由端挠度的预测误差(3%以内)均小于其它理论预测;剪切效应与轴力效应对微梁挠度的贡献为负,且剪切效应对微梁挠度的贡献明显大于轴力效应的贡献.本文模型和结论为微梁生物传感器静态检测信号的解读和有关设计提供了一种新的思路.To meet new detection requirements and achieve high sensitivity,microbeam-based biosensor technique faces challenges in the development of signal interpretation models.Through 3D finite element simulations of the detected quasi-static signals of microbeam under surface adsorption,we revealed an asymmetric distribution characteristic of the microbeam crosssection's warping.However,the existing theoretical models considering shear deformation cannot accurately describe this asymmetric warping.To address this issue,first,we simplified the complete adsorption of molecules as a uniformly distributed surface stress acting on the microbeam's surface and obtained the distribution pattern of warping zero point through 3D finite element simulation.Then,we employed the semi-inverse method of plane elasticity theory to determine the shear stress distribution and shear force that correspond to the asymmetric warping characteristics on the deformed cross-section.This led to an improvement in Timoshenko beam theory and the establishment of a new model to predict the detected quasi-static signals of microbeam.Finally,we validated the analytical model by comparing with experimental results and finite element simulations.The results indicate that the predictions of our improved model agree well with the relevant microbeam experiments.Moreover,within the geometric size ranges employed in the existing adsorption-microbeam static experiments(length-to-thickness ratio of 200-500,length-to-width ratio of 3-7),its prediction error for the microbeam's free-end deflection is less than 3%,which is smaller than that of other theoretical predictions.Additionally,the shear effect and axial force effect negatively impact the microbeam's deflection,with the shear effect having a significantly greater influence than the axial force effect.This model and its conclusions provide a new perspective for interpreting the static detection signals of microbeam biosensors and developing the relevant design.

关 键 词：生物吸附 微梁 表面应力 翘曲效应 信号解读模型 

分 类 号：O341[理学—固体力学] O343.1[理学—力学]