Analysis and Optimal Design of Multi-Layer Structures Subjected to Impulse Loading

摘要

Attenuation of elastic stress waves propagating through a one-dimensional elastic medium is investigated by considering a multi-layer structure situated between free and fixed surfaces. First, a transfer matrix that relates the displacement amplitudes in adjacent layers is derived in the Laplace transform domain, and then applied to analyze the multi-layer structures. A stress transfer function also is developed for the multi-layer structure to provide the stress output at the fixed end under any arbitrary transient load. The analytical solutions of stress at the fixed surface is obtained for both two-layered Goupillaud-type media and a large second layer structure. The analysis shows that when an incident stress pulse passes through a two-layer structure, a reduced stress amplitude and elongated pulse duration could be obtained with proper selection of materials and layer dimensions. In this paper, optimal material requirements are determined for this two-layered structure, based upon an analysis of the stress response at the fixed end. Numerical simulations are also carried out for the purpose of comparison, and are consistent with the analytical solutions.