Discontinuous dynamics with grazing points

Kıvılcım, Ayşegül
The scope of this thesis is to investigate the periodic solutions of impulsive systems with grazing and modeling through differential equations with impulses. By means of differential equations with impacts, the system which is modeled through two distinct differential equations is taken into account and such models are named as models with impact deformations. The surfaces as well as the coefficient of restitution are determined to be dependent on the impact velocity. The simulations are obtained for the relation of the displacement and the restitution with the impact velocity. Analytical formulas are also determined for them. The periodic solutions and their stability are examined analytically for the impulsive systems with the deformable surfaces and the velocity dependent coefficient of restitution and the results are actualized through simulations. The chattering, which was known infinitely many impact occurring in a finite time, is suppressed in the systems by utilizing deformable surfaces and velocity dependent coefficient of restitution. An appropriate definition for the grazing phenomenon is presented. Discontinuous dynamical systems with graziness are obtained. The differentiability and other properties of discontinuous dynamical system are widely investigated. The orbital stability of the periodic solutions are proved. Applying small parameter analysis, the bifurcation of periodic solutions is observed in specific examples. The non-autonomous grazing phenomenon is considered and some sufficient conditions are obtained for the differentiability with respect to initial values. The perturbations around the periodic solutions of those systems are considered and the theoretical results are visualized by simulations.


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Citation Formats
A. Kıvılcım, “Discontinuous dynamics with grazing points,” Ph.D. - Doctoral Program, Middle East Technical University, 2016.