Collaborative Research: Exploration of the Nonlinear Dynamics of NEMS Carbon Nanotube Resonators

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。本研究的目的是提供对静电驱动双夹紧碳纳米管非线性动力学的基本理解，包括松弛的影响，并深入探讨在非线性状态下操作这些器件的后果、优点和缺点。碳纳米管发展的一个主要障碍是缺乏对其动力学行为的了解。由于这些器件由于松弛、中间窗格拉伸和静电力等因素而具有丰富的非线性，因此如何实现可靠的碳纳米管器件存在歧见和未解方程。为了解决这些问题，我们计划开展理论和实验工作，研究由直流静电负载和交流谐波负载叠加而成的大小电负载激励下碳纳米管的动力学。对碳纳米管研究人员至关重要的局部动力学问题，如预测碳纳米管的非线性共振频率、软化和硬化行为、迟滞、一次和二次激励等将被研究。影响碳纳米管谐振器稳定性的全局动力学问题，如动态拉入、带松弛管的卡通、吸引力盆分析等。分析和数值方法，包括微扰技术，降阶模型和射击技术将被利用。实验上，提出了各种光学和电学方法来检测共振频率，监测管的偏转，并捕获拉入的开始，以便对理论工作进行比较和验证。所提出的研究结果将允许在有用的应用中更积极地利用碳纳米管，尽管它们的非线性行为，因为它将提供如何处理它的适当知识。另一方面，可以开辟新的研究途径，有意利用碳纳米管的非线性动力学特性来获得其独特的特性和优势。将揭示在非线性环境下操作NEMS碳纳米管的令人兴奋的可能性，这可能导致发现新的传感器和致动器。此外，本研究应弥合实验测量与理论建模之间的差距，从而正确校准设备并准确估计CNTs的物理性质。这项研究将为来自纽约州立大学和康奈尔大学的研究生提供良好的培训经验。此外，它还将通过美国国家科学基金会资助的宾厄姆顿成功计划培训本科少数民族学生。此外，将与nsf资助的康奈尔纳米制造设施和Kavli研究所建立合作伙伴关系，创建一个纳米Wiki，收集和浓缩纳米设备制造和测量的信息，为国内和国际科学界提供广泛的在线开放访问资源。资金还将允许与康奈尔物理教师研究所合作开发纳米力学的新模块，以传播给纽约州的高中教师。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The objective of the proposed work is to provide fundamental understanding of the nonlinear dynamics of electrostatically actuated doubly-clamped carbon nanotubes, including the effect of slack, and explore in depth the consequences, advantages, and disadvantages of operating these devices in the nonlinear regime. A major obstacle in the development of carbon nanotubes CNTs has been the lack of knowledge of their dynamical behavior. Because of the rich nonlinearities in these devices due to slack, mid-pane stretching, and electrostatic forces, there is ambiguity and unanswered equations of how to realize reliable devices of CNTs. To address these issues, theoretical and experimental works are planned to study the dynamics of CNTs when excited by small and large electric loads composed of a DC electrostatic load superimposed to an AC harmonic load. Local dynamics issues that are vital for CNTs researchers, such as predicting the nonlinear resonance frequencies of CNTs, softening and hardening behaviors, hysteresis, and primary and secondary excitations will be investigated. Global dynamics issues affecting the stability of CNTs resonators, such as dynamic pull-in, snap through of tubes with slacks, and basin-of-attraction analysis will be conducted. Analytical and numerical methods including perturbation techniques, reduced-order models, and shooting techniques will be utilized. Experimentally, various optical and electrical methods to detect the resonance frequencies, monitor the tubes deflections, and capture the onset of pull-in are proposed to enable comparison and validation of the theoretical work. The outcome of the proposed research will allow more aggressive utilization of CNTs in useful applications despite their nonlinear behavior since it will present the proper knowledge of how to deal with it. On the other hand, new research avenues can be opened to deliberately utilize the nonlinear dynamics of CNTs to gain unique features and advantages. Exciting possibilities for operating NEMS CNTs in the nonlinear regimes will be revealed, which can lead to discovery of novel sensors and actuators. Further, this research should bridge the gap between experimental measurements and theoretical modeling, which leads to correct calibration of devices and accurate estimation for the physical properties of CNTs. This research will provide excellent training experience for the graduate students from both institutes (SUNY and Cornell). Also, it will train undergraduate minority students through the NSF-funded Binghamton Success Program. Further, a partnership will be established with the NSF-funded Cornell Nanofabrication Facility and the Kavli Institute to create a Nano Wiki that will collect and condense information on nanoscale device fabrication and measurement for broad on-line open access resource to the national and international scientific community. Funds will also allow partnership with the Cornell Institute for Physics Teachers to develop new modules on nanomechanics for dissemination to New York State high school teachers.