NOISE-INFLUENCED DYNAMICS OF NONLINEAR OSCILLATORS

Loading...
Thumbnail Image
Files
Publication or External Link
Date
2015
Authors
Perkins, Edmon
Advisor
Balachandran, Balakumar
Citation
Abstract
Noise is usually considered detrimental to the performance of a system and the effects of noise are usually mitigated through design and/or control. In this dissertation, noise-influenced phenomena and qualitative changes in responses of nonlinear systems with noise are explored. Here, the author considers a range of nonlinear dynamical systems, including an array of nonlinear, coupled oscillators, a vertically excited pendulum, the Duffing oscillator, and a Rayleigh-Duffing mixed type oscillator. These systems are studied analytically and numerically via stochastic direct numerical integration, and analytically via the Fokker-Planck equation. The array of nonlinear, coupled oscillators is also experimentally studied. The topics covered in this dissertation are as follows: i) the destruction and formation of energy localizations in an array of oscillators, ii) a technique to stabilize an inverted pendulum by using noise, iii) a noise-utilizing control scheme, iv) the effects of noise on the response of a nonlinear system that exhibits chaotic behavior, v) and the effects of phase lag on the information rate of a Duffing oscillator. The understanding gained through this dissertation efforts can be of benefit to a variety of nonlinear systems, including structural systems at the macro-scale, micro-scale, and nano-scale.
Notes
Rights