Controlling wave propagation in one-dimensional structures through topology optimization

Abstract

Research on the control of wave propagation has received continuous attention due to its potentially rewarding applications in the past decades, and numerous methods have been developed for controlling wave propagation in certain materials or structures. Despite previous work has made many innovations in controlling wave propagation, they are limited to the research from a band gap perspective. Herein, this paper presents a gradient-based multi-functional topology optimization for controlling wave propagation in a one-dimensional (1D) structure, which can realize the control of wave propagation from two aspects: band gap and wave propagation speed. To illustrate the method, three case studies are investigated to obtain the following: (1) increasing the band gap width, (2) controlling the wave propagation at target speed, and (3) limiting the propagation of low-frequency waves. By evaluating the results of three case studies, the effectiveness of the proposed topology optimization method is demonstrated. More importantly, the control of wave propagation in the low-frequency range in Case III lends new insight into the vibration isolation structure in engineering applications.