Fast design of non-uniform acoustic waveguides with prescribed eigenfrequencies

Abstract

In this article we address the issue of finding acoustic and elastic resonator shapes corresponding to given eigenfrequencies. This problem has a wide range of applications spanning from ultrasonics through the music acoustics to metamaterials. We employ the previously published solution to the Webster horn equation and use it to train an artificial neural network to solve the inverse eigenvalue problem. Subsequently, it is shown how the isospectrality and scalability properties might provide a whole class of fast designed resonator shapes.