Analytical modeling of a cylindrical acoustic-electric transmission channel using two-port network transfer matrices-based method

Abstract

Modeling cylindrical wave propagation is paramount in several applications, ranging from data transmission through curved barriers to studies in seismic analysis. To obtain solutions, numerical methods, such as the finite element method (FEM), are often employed. However, depending on the frequencies, they may become impractical since very refined meshes could be required, leading to high computational efforts. Within this context, analytical approaches based on transfer matrices emerge as prominent options, since they take advantage of matrix operations. Therefore, the propagation of cylindrical waves in elastic and piezoelectric materials is modeled in this paper using the two-port network method based on ABCD parameters. These parameters were validated by modeling the transmission of acoustic signals through cylindrical barriers using a pair of piezoelectric transducers. In the beginning analysis, the internal radius was varied. At high radii, slight changes were observed in the shape of the resultant waveform, in line with the intuition of a plane wave condition. Further analyses were carried out by comparisons with FEM simulations. Finally, an experimental setup was prepared, and the amplitude-increase behavior predicted in the multi-layer configuration models could be experimentally observed. Overall, good agreement between the results was obtained, validating the proposed lightweight method.