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.

中文翻译：

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通过拓扑优化控制一维结构中的波传播

摘要 在过去的几十年中，由于其潜在的有益应用，波传播控制的研究受到了持续关注，并且已经开发了许多方法来控制某些材料或结构中的波传播。尽管以前的工作在控制波传播方面取得了许多创新，但它们仅限于从带隙角度进行的研究。在此，本文提出了一种基于梯度的多功能拓扑优化控制一维（1D）结构中的波传播，可以从带隙和波传播速度两个方面实现对波传播的控制。为了说明该方法，研究了三个案例研究以获得以下结果：（1）增加带隙宽度，（2）控制波以目标速度传播，(3) 限制低频波的传播。通过评估三个案例研究的结果，证明了所提出的拓扑优化方法的有效性。更重要的是，案例 III 中低频范围内波传播的控制为工程应用中的隔振结构提供了新的见解。