Elastic wave transmission control using band gap and impedance matching

Abstract

A finite-sized periodic structure made of specially-configured element unit cells is proposed to control elastic wave transmission by using the band gap phenomenon and the impedance matching concept. The proposed unit cell consists of two impedance-mirrored elements, each of which has a mirrored impedance distribution of the other while each element is determined by the impedance matching concept. The mirroring approach can preserve the excellent transmission performance of the single impedance-matching element because the mirrored element is the impedance-reversed system of the original matching element. With this reversing, the overall impedance contrast within the unit cell is also realized which is necessary to form stop bands in a periodic structure. By using these characteristics of the proposed impedance-mirrored structure, the design of frequency filters is considered. First, a single frequency pass filter of total transmission at a target frequency is realized by the proposed periodic matching elements. The periodic matching element is long enough to keep the pass band between the adjacent stop bands by periodic stacking of the unit cells. When a frequency band pass filter is to be realized, the matching element having a non-uniform impedance distribution is developed. The distribution is so engineered as to maximize wave transmission in the pass band and also to minimize transmission in its adjacent stop bands. To obtain an optimal impedance distribution in the matching element, a sizing optimization problem is formulated in which the impedance values of the discretized layers of the matching element are used directly as continuously-varying design variables. The extraordinary performance of the frequency band pass filter constructed by the impedance mirroring approach, such as high transmission with large bandwidth and sharp roll-off is found to be acheved. Furthermore, the proposed approach is applied to deal with an engineering problem to design matching elements between an ultrasound transducer and human skin for super transmission. After the matching elements are designed theoretically by the proposed approach, they are realized with specially-engineered metamaterials.