Nonlinear Vibration and Stability Analysis of Nano-scale Elastic Beam-type Structures

纳米级弹性梁型结构的非线性振动与稳定性分析

• 批准号: RGPIN-2014-06242
• 负责人: Esmailzadeh, Ebrahim
• 金额: $ 1.97万
• 依托单位: University of Ontario Institute of Technology
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=567684
• 关键词: Nonlinear; Vibration; Stability; Analysis; Nano

Nanobeams and Nanotubes are considered nowadays to have wide range of applications in modeling of biosensors, medicine carriers, resonators, artificial tiny blood vessels, Nano-switches and Nano-power generators. Mechanical and electronic properties of almost all the nanostructures are highly influenced by their nonlinear vibration signatures and resonant frequencies. This research is aimed to develop a reliable model to consistently simulate the large-amplitude nonlinear vibration of elastically surrounded nanotubes and nanobeams. A comprehensive study is sought to investigate the unexplored aspects of nonlinear vibration of nanostructures, since the type and strength of nonlinearities are fundamentally different from those of the macro-scale structures. In this research program I will investigate four main issues under a unified framework of: a) Introducing accurate modeling and new analytical solutions for vibration analysis of nanotubes and nanobeams, b) Sensitivity analysis of nanostructure parameters considering different types of nonlinearities, c) Stability analysis and performance study of vibrating nanostructures, and d) Chaos prediction and control of potential chaotic behavior in nanostructures. The essential foundation of this proposal is based on my recent contributions in the modeling and analysis of nonlinear vibrating systems and also performance verification with recent reported experimental results by other researchers in this field. One of the goals of this research is to investigate the interactions of different types of nonlinearities in Nano-scale and also determine the potential of either resonance magnification or cancelation. A general variational-based approach will be developed for the straight, curved and wrinkled nanobeams. Modeling of a wrinkled nanostructures employing the theory of non-uniform rational basis spline (NURBS) is another objective and contributions of this research. The undiscovered dynamic behavior of nanostructures is identified when the geometrical nonlinearities tend to combine with other nonlinear phenomena such as the fringing and Casimir effects. Free vibration, as well as, the harmonic and stochastic vibrations of such nanostructures will be simulated. Different types of possible resonant conditions, including the primary and secondary resonances, as well as the internal resonant cases are considered. The main harmonics together with the sub-harmonic and super-harmonic responses are obtained. A bifurcation analysis is carried out and the stability of periodic and quasi-periodic solutions for nanobeams and nanotubes will be investigated. The effects of interactive nonlinear forces, size, surface and the geometrical conditions on the vibration behaviors of these structures will thoroughly be examined. The outcome of this research will not only enhance the frontier of knowledge for more realistic models and solutions, but also greatly benefit the Canadian and international industries especially in three categories of electric circuits, tissue engineering and regenerative medicine.

如今，纳米束和纳米管被认为在生物传感器、药物载体、谐振器、人造微血管、纳米开关和纳米发电机的建模中具有广泛的应用。几乎所有纳米结构的机械和电子特性都受到其非线性振动特征和共振频率的高度影响。这项研究的目的是开发一个可靠的模型来一致地模拟弹性包围的纳米管和纳米梁的大振幅非线性振动。由于非线性的类型和强度与宏观尺度结构根本不同，因此寻求进行全面的研究来研究纳米结构非线性振动的未探索方面。在本研究计划中，我将在统一框架下研究四个主要问题：a）为纳米管和纳米梁的振动分析引入精确建模和新的分析解决方案，b）考虑不同类型非线性的纳米结构参数的敏感性分析，c）稳定性分析振动纳米结构的性能研究，以及 d) 纳米结构中潜在混沌行为的混沌预测和控制。该提案的基本基础是基于我最近在非线性振动系统建模和分析方面的贡献，以及该领域其他研究人员最近报告的实验结果的性能验证。这项研究的目标之一是研究纳米尺度中不同类型非线性的相互作用，并确定共振放大或消除的潜力。将为直的、弯曲的和褶皱的纳米束开发一种基于变分的通用方法。采用非均匀有理基样条 (NURBS) 理论对皱纹纳米结构进行建模是本研究的另一个目标和贡献。当几何非线性倾向于与其他非线性现象（例如边缘效应和卡西米尔效应）结合时，就会发现纳米结构未被发现的动态行为。将模拟此类纳米结构的自由振动以及简谐振动和随机振动。考虑了不同类型的可能谐振条件，包括初级和次级谐振以及内部谐振情况。获得主谐波以及次谐波和超谐波响应。进行分岔分析，并研究纳米束和纳米管的周期和准周期解的稳定性。将彻底检查相互作用的非线性力、尺寸、表面和几何条件对这些结构的振动行为的影响。这项研究的成果不仅将增强更现实的模型和解决方案的知识前沿，而且还将极大地惠及加拿大和国际行业，特别是在电路、组织工程和再生医学三个领域。