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，纳米梁和纳米管被认为在生物传感器，药物载体，谐振器，人造小血管，纳米转换和纳米功率发生器的建模中都有广泛的应用。几乎所有纳米结构的机械和电子特性都受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，以始终模拟弹性包围的纳米管和纳米梁的大振幅非线性振动。试图进行一项全面的研究来研究纳米结构非线性振动的未开发方面，因为非线性的类型和强度与宏观结构的类型和强度根本不同。在该研究计划中，我将在一个统一的框架下研究以下统一框架：a）引入准确的建模和新的分析解决方案，用于纳米管和纳米梁的振动分析，b）纳米结构参数的敏感性分析，考虑不同类型的非线性类型的稳定性分析和稳定性研究的稳定性研究的振动nanostruction和dectifter nanos prandos and ana ann ann ann ann ann ann chaaos and ana chaaos和deas conaos的敏感性分析。该提案的基本基础是基于我在非线性振动系统的建模和分析中的最新贡献，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级不同类型的非线性的相互作用，并确定共振放大或取消的潜力。将为直，弯曲和皱纹的纳米梁开发一种一般基于变异的方法。采用非均匀理性基础样条（NURB）理论的皱纹纳米结构的建模是这项研究的另一个客观和贡献。当几何非线性倾向于与其他非线性现象（例如边缘和卡西米尔效应）结合时，可以确定纳米结构的未发现动态行为。将模拟自由振动以及此类纳米结构的谐波和随机振动。考虑了不同类型的可能的共振条件，包括主要和次要共振以及内部共振病例。获得了主要谐波以及亚谐波和超谐波反应。进行分叉分析，并将研究对纳米梁和纳米管的周期性和准周期溶液的稳定性。相互作用的非线性力，大小，表面和几何条件对这些结构振动行为的影响将得到彻底研究。这项研究的结果不仅将增强知识的前沿，以实现更现实的模型和解决方案，而且还可以极大地使加拿大和国际工业受益，尤其是在三类电路，组织工程和再生医学的三类中。