Abstract The main aim of this paper is to present a topology optimization method for a local resonator, in order to tailor flexural bandgaps in plate structures. The local resonator is required to be designed systematically in order to tailor the bandgap at the desired frequency range. In previous studies, beam or plate-like resonators were usually used for the design purpose, but the freedom of design is limited particularly when the allowable dimensions are highly limited. Regarding the design issue, this research presents a systematic method using topology optimization to design the local resonator with the maximized bandgap at the target frequency. A plate-like resonator is parameterized to fully exploit the allowable design space of a unit cell. The topology optimization is carried out with the non-gradient based algorithm i.e. simulated annealing (SA). To assist the SA, which requires a large number of function evaluations, two computationally efficient finite element (FE) approaches, namely plate modelling and the reduced Bloch mode expansion, are combined with the topology optimization. In addition, numerical techniques are applied to solve issues arising in the design process (i.e. design disconnection, hinged design, and design redundancy). Numerical examples demonstrate the effectiveness of the presented method for creating bandgaps at frequencies below 500 Hz. The results exhibit increases in vibration isolation up to 20 dB at the designed frequencies.

中文翻译：

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使用拓扑优化来设计板结构中的带隙的局部谐振器

摘要 本文的主要目的是提出一种局部谐振器的拓扑优化方法，以定制板结构中的弯曲带隙。需要系统地设计局部谐振器，以便在所需频率范围内调整带隙。在以前的研究中，梁或板状谐振器通常用于设计目的，但设计的自由度受到限制，特别是当允许的尺寸非常有限时。关于设计问题，本研究提出了一种使用拓扑优化的系统方法来设计在目标频率下具有最大带隙的局部谐振器。板状谐振器被参数化以充分利用单元的允许设计空间。使用基于非梯度的算法进行拓扑优化，即 模拟退火 (SA)。为了协助需要大量函数评估的 SA，两种计算效率高的有限元 (FE) 方法，即板建模和减少的 Bloch 模式扩展，与拓扑优化相结合。此外，应用数值技术解决设计过程中出现的问题（即设计断开、铰链设计和设计冗余）。数值例子证明了所提出的方法在低于 500 Hz 的频率下创建带隙的有效性。结果表明，在设计频率下，隔振性能提高了 20 dB。与拓扑优化相结合。此外，应用数值技术解决设计过程中出现的问题（即设计断开、铰链设计和设计冗余）。数值例子证明了所提出的方法在低于 500 Hz 的频率下创建带隙的有效性。结果表明，在设计频率下，隔振性能提高了 20 dB。与拓扑优化相结合。此外，数值技术被应用于解决设计过程中出现的问题（即设计断开、铰链设计和设计冗余）。数值例子证明了所提出的方法在低于 500 Hz 的频率下创建带隙的有效性。结果表明，在设计频率下，隔振性能提高了 20 dB。