Study On One Dimension Wave Equation Of A Nonlinear Elastic Rod

As the development of modern science and technology, non-linear science has obtained rapidly progress and its essence was discovered and explained continually. Nonlinear wave is an important part of it. In this dissertation wave equation of a nonlinear elastic rod in one dimension is researched.This dissertation consists of 4 chapters. In the first chapter a comprehensive study for theory of nonlinear wave in solid medium is presented. In chapter 2 Hamilton principle, Solitons, Reductive perturbation methods and Complete approximate method are presented. In chapter 3 the nonlinear wave equation of longitudinal oscillation of a nonlinear elastic rod with lateral inertia is obtained from the Hamilton principle. By using Reductive perturbation methods and Complete approximate method, Burgers equation, KdV equation, KdV-Burgers equation, NLS equation and a strongly nonlinear equation are established, which describes the wave motion of the rod. The solutions of the equations are presented. Lastly, in this dissertation the conclusion and prospects of researches are presented.