Sample transfer function estimation of high-frequency elastic waves using Hopkinson bar

Hopkinson pressure bar is a commonly used technique to test the response of a specimen to shock load under constant strain rate to determine its material parameters. In addition to that, we propose that the Hopkinson bar apparatus can be employed to test the response of the specimen in the sense of frequency analysis; that is, specimens made of a complex metamaterial could behave as a filter of specific frequencies. Here, several difficulties arise. The structure of the metamaterial affects only those waves that have a wave length comparable to the specific length in the metamaterial of the specimen. However, the bar geometry of the apparatus itself behaves as a low-pass filter, so the high frequencies are attenuated with distance traveled. Hence, here we have the situation that the longer the specimen is, we lose the ability to investigate high frequencies, and, at the same time, the shorter the specimen is, the higher the lowest affected frequency is. Our contribution is to find a compromise for the length of the sample and to design a high-frequency testing method for such an investigation of metamaterials.