Parametrically Excited Nonlinear Gyroscopic Systems

参数激励非线性陀螺仪系统

• 批准号: 0084944
• 负责人: N. Sri Namachchivaya
• 金额: $ 18.06万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-15 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0084944&HistoricalAwards=false
• 关键词: Parametrically; Excited; Nonlinear; Gyroscopic; Systems

PI: N. Sri NamachchivayaUniversity of Illinois @ Urbana-ChampaignProposal (# 0084944) Title: Parametrically Excited Nonlinear Gyroscopic SystemsThe overall goal of our proposed investigation is to formulate and develop methods to study the long term effects of small dissipative, symmetry-breaking and time-dependent perturbations on nonlinear gyroscopic systems, particularly the dynamics of rotating shafts and pipes conveying fluid. This proposal outlines a unified framework to study nonlinear systems with either periodic} or stochastic perturbations. An understanding of the dynamics of parametrically excited gyroscopic systems necessitates a study of the complex interactions between time-dependent inputs, symmetries, and nonlinearities. Our approach will consist of the application of some recent theories of deterministic and stochastic dimensional reduction to relevant nonlinear gyroscopic models. The proposed work consists of essentially four components: appropriate modelling, further development of some theoretical considerations, numerical algorithms, and experimental verification. The outcome will be a greatly-enhanced understanding of the stability and global dynamics of gyroscopic systems under dissipation and time-dependent perturbations. In the deterministic context, we will be able to predict global dynamics and the mechanisms which give rise to global bifurcations in gyroscopic systems. We shall also examine stabilization of gyroscopic systems by periodic excitations when the excitation frequency is slightly above a certain resonance frequency.In the stochastic context, we will be able to compute a number of standard stability indices (e.g., stationary measures and exit times) in a theoretically correct and computationally efficient way. In the final part of this research, dynamic experimentswill be conducted on a rotating shaft to verify the theoretical results obtained. These dynamics experiments will locate the stability boundaries and examine the nature of the nonlinear response. The numerical and experimental results will, in turn, guide the theories to incorporate any new phenomena observed.

PI：N.SRI NamachchivayaUniversity of Illinois@Urbana-ChampaignProposal(#0084944)标题：参数激励的非线性陀螺系统我们提出的研究的总体目标是建立和发展方法来研究微小的耗散、对称破缺和依赖时间的扰动对非线性陀螺系统的长期影响，特别是旋转轴和输送流体的管道的动力学。这一建议概述了一个研究周期或随机扰动的非线性系统的统一框架。要理解参激陀螺系统的动力学，就必须研究依赖时间的输入、对称性和非线性之间的复杂相互作用。我们的方法将包括将最近的一些确定性和随机性降维理论应用于相关的非线性陀螺模型。建议的工作基本上由四个部分组成：适当的建模、一些理论考虑的进一步发展、数值算法和实验验证。其结果将大大增强对陀螺系统在耗散和依赖于时间的扰动下的稳定性和全局动力学的理解。在确定性的背景下，我们将能够预测陀螺系统的全局动力学和导致全局分叉的机制。我们还将研究当激励频率略高于某个共振频率时，陀螺系统在周期激励下的稳定性。在随机环境中，我们将能够以理论上正确和计算有效的方式计算一些标准稳定性指标(例如，平稳度量和退出时间)。在本研究的最后部分，将在转轴上进行动力学实验，以验证理论结果的正确性。这些动力学实验将定位稳定边界，并检查非线性响应的性质。数值和实验结果将反过来指导理论纳入所观察到的任何新现象。