The contact force in generalized hertz type systems and solitary waves
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The studies of contact mechanics and solitary waves have long been exciting subjects in both engineering and physics. Somewhat surprisingly, in view of the vital importance of the subjects, theoretical progress has been few and far between. In this work, we first discuss a way to investigate the contact force between two purely elastic paraboloidal solids. The contact force turns out to be strongly nonlinear. We next study the dynamics of a 1D granular system composed of the above mentioned solids. Both analytical and numerical methods have been employed. It is not obvious that intuitive reasoning is effective for these strongly nonlinear problems. In preparing this thesis, attempts have nevertheless been made to make the presentation as intuitively meaningful as possible. We next present a scaling law that determines the relation between the spatial extent of a solitary wave and the strength of the nonlinearity of the granular contacts. This work is followed by a discussion on the possibility of existence of an equilibrium-like state in certain strongly nonlinear systems, such as granular alignments. In closing, a number of interesting studies of solitary wave bearing cases have been explored, which indicate the possibility of developing potential technological applications. References have been listed alphabetically at the end of each chapter appendices are placed at the end of the thesis. It is inevitable that errors have remained undetected. And it has been challenging to use a consistent notation. I will be grateful to be made aware of any such errors that readers may discover.