With the advance of additive manufacturing, many researchers are increasingly interested in planar acoustic lenses that are not only easier to fabricate than typical convex/concave lenses, but also have excellent imaging performance. However, the planar acoustic lenses reported so far cannot work for a short-duration pulse used in conventional imaging systems due to their inherent dispersive characteristics. This study addresses the challenge by devising a transient topology optimization formulation to design a planar acoustic lens that works effectively for a short-duration pulse. A planar lens consists of two materials where optimal combination and distribution are obtained with a crisp interface via the level-set method. Design is based on the transient acoustic responses, which are calculated from a time-dependent acoustic model solved by the Newmark method. The proposed method uses the area-fraction approach to compute the acoustic properties of a cut element by the interface. A localizing time-window function is introduced so that acoustic energy can be focused within the desired time range as much as possible. We obtain optimum design solutions designed with the proposed method and verify its effectiveness through the numerical investigations.

中文翻译：

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短时脉冲工作的平面声透镜的瞬态水平集拓扑优化

随着增材制造技术的进步，许多研究人员对平面声透镜越来越感兴趣，这种透镜不仅比典型的凸/凹透镜更容易制造，而且具有出色的成像性能。然而，由于其固有的色散特性，到目前为止报道的平面声透镜不能用于常规成像系统中使用的短时脉冲。这项研究通过设计一种瞬态拓扑优化公式来设计一种对短时脉冲有效工作的平面声透镜，从而解决了这一挑战。平面透镜由两种材料组成，可以通过水平设置方法获得具有清晰界面的最佳组合和分布。设计基于瞬态声学响应，它们是通过使用Newmark方法求解的随时间变化的声学模型计算得出的。所提出的方法使用面积分数方法通过界面来计算切割元件的声学特性。引入了本地化的时间窗口功能，以便可以将声能尽可能地集中在所需的时间范围内。我们获得了用所提出的方法设计的最佳设计解决方案，并通过数值研究验证了其有效性。