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Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
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MC 5501 and MS Teams (please email amgrad@uwaterloo.ca for the meeting link)
Iyi Oluyemi | Applied Mathematics, University of Waterloo
Almost-Sure Stability of a Noisy Autoparametric Vibration Absorber
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.
Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
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