Almost-Sure Stability of a Noisy Autoparametric Vibration Absorber
| dc.contributor.author | Oluyemi, Momoiyioluwa | |
| dc.date.accessioned | 2022-12-13T21:23:27Z | |
| dc.date.available | 2022-12-13T21:23:27Z | |
| dc.date.issued | 2022-12-13 | |
| dc.date.submitted | 2022-12-07 | |
| dc.description.abstract | This thesis investigates the almost-sure stability of the single mode solution of a two degree-of-freedom, noisy, nonlinear autoparametric system. While only the first mode is forced in such a system, the nonlinear coupling often transfers energy to the second mode. Equations of motion of autoparametric systems model the dynamics of a number of structural and mechanical systems, such as, a randomly excited and initially deformed shallow arch, a suspended elastic cable driven by planar excitation, or a vessel subject to longitudinal wave action. To keep things as simple as possible, we consider a very simple system, namely, a type of autoparametric vibration absorber with randomly excited base - a pendulum attached to a mass-spring oscillator. Under the assumption of small random perturbations and small damping, the maximal Lyapunov exponent which determines the almost-sure stability of the single mode solution is calculated. Putting the maximal Lyapunov exponent to zero provides the second-order approximation of the almost-sure stability boundary in terms of the excitation intensity and the dissipation coefficients. A plot of this stability boundary reveals several trends of practical importance to engineering applications. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/18954 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.title | Almost-Sure Stability of a Noisy Autoparametric Vibration Absorber | en |
| dc.type | Master Thesis | en |
| uws-etd.degree | Master of Mathematics | en |
| uws-etd.degree.department | Applied Mathematics | en |
| uws-etd.degree.discipline | Applied Mathematics | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws-etd.embargo.terms | 0 | en |
| uws.contributor.advisor | Namachchivaya, Navaratnam Sri | |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |