DynSyst_Special_Topics: New Challenges in Non-Smooth Dynamical Systems - Experiments and Analysis

Duke University, Durham NC

Investigators

Abstract

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). This proposal puts forward closely coupled studies involving experiments, modeling, analysis, and numerical simulations of fundamental hybrid mechanical systems with piecewise smooth motion and discrete impact events. The investigators will use recent developments in the analysis of bifurcations in non-smooth dynamics as a starting point for the work. The approach taken in this project is to expand the understanding of the dynamics, stability and bifurcations of systems with impacts by detailed exploration of two prototype problems: (i) the driven motion of tethered particles and (ii) the impacting pendulum. These problems provide solid testbeds for the studies in response to recent interest in bifurcations due to non-smooth forcing and collisions in multi-element systems. These problems have significance as basic components in larger-scale mechanical and industrial systems. They are also very well suited to experimental studies, allowing for the validation of numerical simulations and simplified mathematical models. This project will advance the understanding of classes of mechanical systems ubiquitous in natural and industrial settings. Potential results on stability and bifurcations will allow for more efficient, productive and reliable operating conditions. Moreover, they fit into a long-term program for the study of the feasibility of damage detection via system response to impactive forcing. Namely, we seek to demonstrate that bifurcations and response to impactive forcing can be used to diagnose internal structural defects as a means of nondestructive testing and possible control and suppression of instabilities. The proposal builds a new collaboration between researchers in engineering and applied mathematics and will incorporate graduate and undergraduate student training in an interdisciplinary research program that will develop coordinated advanced skills in engineering and nonlinear dynamics. There are plans for ensuring the participation of under-represented groups, building on recent successes. Results from this project will be disseminated through journal publications in engineering and applied dynamical systems, presentations at research conferences and through a project web page and via connections with Duke University's Center for Nonlinear and Complex Systems. Research will be augmented by improvements in student training in the development of courses in engineering and applied mathematics.