Evolution Of Nonlinear Strain Wave In Waveguides

In this thesis, the numerical methods are developed to investigate the evolution of nonlinear strain wave in two kinds of waveguides--elastic rod and layer medium overlying a half space.Firstly, the evolution of nonlinear wave in elastic rod is analyzed numerically. Based on previous work, the Murnaghan model and Hamilton variation principle are used to build a new model equation of nonlinear wave propagation in the elastic rod embedded in an external medium, and obtain the model equation of nonlinear wave propagation in the free elastic rod under special case. At the same time, the evolutions of solitary wave in free elastic rod, elastic rod embedded in an external medium and elastic rod partially embedded in an external medium are simulated numerically by using finite difference method.The calculation results show that the solitary waves can propagate stably in free elastic rod, namely, the shape, amplitude and velocity of the solitary wave keep invariant in the process of propagation. Besides, the amplitudes attenuate gradually and asymmetrical characteristics appear to solitary waves when they propagate in the elastic rod embedded in an external medium. In exposed part of the elastic rod embedded in an external medium, however, the solitary waves can propagate stably but the amplitudes attenuate gradually and asymmetrical characteristics appear to them after entering the part embedded in an external medium.Secondly, the evolutions of nonlinear waves in layer medium overlying a half space are simulated numerically. Model equation of nonlinear longitudinal and transverse waves in layer medium overlying a half space is developed by using Murnaghan model and Whitham thought. Evolutions of nonlinear longitudinal and transverse waves in layer medium overlying a half space are also simulated numerically. The results indicate that, in same layer (same coefficient of dispersion), longitudinal wave with smaller amplitude will evolve gradually and disappear finally; those with larger amplitude will evolve gradually into one solitary wave or two solitary waves, and those with largest amplitude will evolve gradually into solitary wave train. In different layer (different coefficient of dispersion), however, the longitudinal wave with same kind of amplitude will evolve gradually into one solitary wave, or two solitary waves, or solitary wave train, or disappearance. It's worth noting that stronger frequency dispersion is not of benefit to longitudinal wave to evolve into solitary wave. Furthermore, physical factors only play a role in accelerating or slowing down the process but have no effect on the results of evolution of longitudinal wave. The evolution of nonlinear transverse wave is similar to that of longitudinal wave except the condition, processes and results of evolution needed.The changes of shapes, amplitudes and velocities of nonlinear strain waves can reflect internal structure characteristics of waveguide material when they propagate in waveguides. So, the nonlinear strain waves propagated in the elastic rod embedded in an external medium and layer medium overlying a half space studied in this thesis are significant in theory to measure the quality of anchor rod anchor and the earthquake wave propagated in crusted zone.