Dynamics of Noisy Nonlinear Mechanical Systems

本研究的总体目标是制定和发展的方法来分析噪声，对称性和旋转和陀螺系统中固有的非线性之间的复杂的相互作用，特别是动态的旋转柔性盘和旋转shaft.The方法包括一个合理的低维随机模型，系统地捕捉噪声机械系统的基本特征的建设。所提出的工作的基础是收集的极限理论的随机过程建模一类工程问题占主导地位的哈密顿动力学。对于简化模型，人们寻求响应和稳定性的标准统计测量;例如，平均退出时间，李雅普诺夫指数和平稳措施，使它有可能设计可靠的工程系统。拟议的工作将是跨学科的，从建模和新的分析技术到实验验证。我们计划将在拟议计划中开发的创新理论和模拟转移到工业中，这将允许改进各种旋转系统的设计和更高的性能。拟议工作的最终成果的一个组成部分将是web-基于模拟器，用于高级本科生和研究生课程，并为工业设计师提供预测工具，以避免不必要的行为。这将增强噪声对真实的工程问题的影响的视觉理解。

The overall goal of this investigation is to formulate and develop methods to analyze the complex interactions between noise, symmetries, and nonlinearities inherent in rotating and gyroscopic systems, particularly the dynamics of spinning flexible discs and rotating shafts.The approach consists of a rational construction of low-dimensional stochastic models that systematically capture essential features of noisy mechanical systems. The basis of the proposed work is a collection of limit theories for stochastic processes which model a class of engineering problems with dominant Hamiltonian dynamics. For the reduced model, one seeks standard statistical measures of response and stability; e.g., mean exit times, Lyapunov exponents and stationary measures, so that it may be possible to design reliable engineering systems. The proposed work will be a cross-disciplinary one, spanning the spectrum from modeling and novel analytical techniques to experimental verification.We plan to transfer to industry innovative theory and simulations developed in the proposed program which will allow improved design and greater performance of various rotating systems.An integral part of the final outcome of the proposed work will be web-based simulators to be used in senior undergraduate and graduate courses and to provide industrial designers with a predictive tool to avoid unwanted behavior. This will enhance visual understanding of the effect of noise on real engineering problems.