P2F-4 Frequency Selective Wave Propagation in Graded Materials

Let´s consider a mechanical stress pulse propagating in an elastic medium. When this pulse encounters a material or phase interface, which generally represents a change of the acoustic impedance, the pulse is split up into two parts. The first part is propagating further into the new material and the second part is reflected. The amplitude ratio of the reflected and the transmitted part is governed by the normalized difference of the acoustic impedance only, provided that the impedance change is a pure step function in space. If the acoustic impedance change is broadened spatially, the ratio of the transmitted and reflected part becomes frequency dependent and the effect can therefore be used for filtering, damping, acoustic isolation, and/or spectrum analysis purposes or for quantitative analysis of interfaces. The effect is of growing importance for micro- and nanostructures since the relative size of the interface layers is generally larger than in macroscopic structures. In this work, a pulse propagating in a linear elastic graded material is investigated with one-dimensional simulations. The numerical scheme is based on the Finite-Difference Time-Domain method (FDTD). The validation of the numerical model is carried out by comparing the simulated pulse propagation stress history with an analytical solution based on Chiu et al. [1].