Dynamics of Noisy Nonlinear Mechanical Systems

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

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.