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: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=588893
• 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.

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。几乎所有的纳米结构的机械和电子性质都受到其非线性振动特征和共振频率的高度影响。本研究的目的是建立一个可靠的模型，以一致地模拟弹性包围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的非线性有着根本的不同，因此，本文试图对纳米结构的非线性振动进行全面的研究。在这个研究项目中，我将在一个统一的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的建模和新的解析解，B）考虑不同类型的非线性的纳米结构参数的灵敏度分析，c）振动纳米结构的稳定性分析和性能研究，以及d）混沌预测和控制潜在的混沌行为的纳米结构。 这个建议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道的实验结果的性能验证。本研究的目标之一是研究纳米尺度下不同类型的非线性之间的相互作用，并确定共振放大或抵消的潜力。一个通用的基于变分的方法将开发为直，弯曲和褶皱的纳米梁。利用非均匀有理基样条（NURBS）理论对褶皱纳米结构进行建模是本研究的另一个目标和贡献。当几何非线性与其他非线性现象如边缘效应和卡西米尔效应联合收割机结合时，纳米结构的未被发现的动力学行为被确定。自由振动，以及这种纳米结构的谐波和随机振动将被模拟。不同类型的可能的谐振条件，包括初级和次级谐振，以及内部谐振的情况下被认为是。得到了系统的主谐波、次谐波和超谐波响应。进行了分岔分析和稳定性的周期和准周期解的纳米梁和纳米管将进行调查。将深入研究相互作用的非线性力、尺寸、表面和几何条件对这些结构振动行为的影响。 这项研究的成果不仅将提高知识的前沿更现实的模型和解决方案，而且也大大有利于加拿大和国际产业，特别是在三个类别的电路，组织工程和再生医学。