Stress Wave Propagation through non-Goupillaud type Elastic Layered Media

This project considers one-dimensional stress wave propagation in a two-layered elastic strip of finite length, subjected to given initial and boundary data. The layers are assumed of unequal travel time known as non-Goupillaud type layered media, which is realized by unequal layer length but same wave speed. Our main objective is to explore the stress wave propagation along the finite strip, and obtain the formulas for the stress in each layer. We consider layer length ratios of the form 1 : 2^k, where k is an integer, and obtain recurrence relations by generalizing the pattern of the stress wave propagation.

We then solve the recurrence relations for the case that corresponds to the layer length ratio of 1:2, by converting it to the previously studied case of the three layered media of equal travel-time. Based on a  mathematical model involving the method of characteristics, we solve the case analytically, and optimize the results.