NEMS/MEMS谐振器非线性振动的解析逼近与稳定性研究

With the NEMS/MEMS technology infiltrating into our daily life, stability and reliability of NEMS/MEMS devices have been attracted attention. Dynamical behavior of NEMS/MEMS resonators which are the core assemblies of MEMS/NEMS devices directly affect their performace. Therefore, it is important to understand the relationship of the NEMS/MEMS resonators’ nonlinear dynamical response with surface effect, molecular mass and stiffness due to molecular adsorption, coupled effect of electromechanical field, etc. This project is focused on constructing the improved continuum models of NEMS/MEMS resonators to character nonlinear oscillation, and modeling multiscale/molecular modeling-based simulations, with considering effect of molecular mass and energy due to molecular adsorption. What’s more, this project intends to develop brief and highly accurate analytical approximate technology, in order to solve the presented models and determine the stability, and illustrate nonlinear dynamical mechanism of NEMS/MEMS resonators. Finally, this project would elucidate the principle of establishing analytical approximate solutions. The present results could qualitatively guide design, optimization, and application of NEMS/MEMS devices. Furthermore, the proposed results could also be used to study other structures'nonlinear oscillation models.

随着NEMS/MEMS技术渗透到社会生活的各个领域，其工作的可靠性及稳定性日益受到人们的关注。微纳机电谐振器动力学响应直接影响微纳米产品的工作效果，因而研究清楚微纳机电谐振器的非线性动力学响应与表面效应、吸收分子质量与能量、机电耦合作用等物理和几何量的依赖关系，揭示微纳机电谐振器的物理本质，是成功设计及应用微纳机电器件的关键。本项目将考虑这些主要因素,建立改进的微纳机电系统连续体非线性振动模型、考虑吸收分子效应的多尺度模型。研发简洁高效、高精度的解析逼近技术求解这些模型并判别解的稳定性，揭示微纳机电谐振器结构非线性动力学响应机理。本项目将阐明解析逼近技术构造原理。研究成果可以为微纳机电器件的设计、优化及应用提供理论指导，还可推广用于研究其他结构非线性振动模型的求解与稳定性判别。

近些年来，微/纳机电系统技术得到了迅猛发展，微系统器件（如微传感器、微执行器、微型机器人、微型飞行器等）已经在汽车、航空航天、通信、自动控制、军事、生物、医药等领域得到了广泛的应用。每年MEMS/NEMS器件的销售量成倍增长，随着硅微机械加工技术的发展，其未来的市场前景更为广阔。然而，还有许多问题没有研究清楚：表面效应、初始缺陷等对于系统的影响程度理论上还没有定论，实验与理论结果仍然有很大分歧，值得进一步从理论上进行研究。针对MEMS/NEMS谐振器非线性动力学方面未解决的问题，本项目针对不同尺寸等条件下，建立了考虑主要影响因素的较符合实验结果的改进连续体非线性振动参数化模型。研发了简洁高效、高精度的解析逼近技术来求解这些模型问题，揭示MEMS/NEMS谐振器结构非线性动力学响应机理。通过本项目的运行，对于典型的MEMS/NEMS器件结构，给出显式的逼近解反映出响应与系统参数之间的依赖关系，得到了尺度效应、环境温度、模型端部条件等对于MEMS/NEMS结构的动力学行为影响程度。另外，本项目还研究了具有初始缺陷的MEMS/NEMS结构，得到了初始缺陷对吸合极限参数的影响，使得本项目的研究更贴近实际。本项目给出了解析逼近技术构造原理，编写出了相应的程序模块。本项目的研究成果可用于指导MEMS/NEMS器件的设计、优化及应用，从而降低研发成本，提高研发效率。