Incorporating the porous characteristics inspired by bio-materials into the phononic crystal (PnC) structure may lead to a more extensive range of properties or new functional spaces. On the contrary, the mechanical deficiencies in PnCs, apart from the band gap (BG) characteristics, pose challenges for engineering applications. Therefore, a floating projection topology optimization (FPTO) framework is proposed here to design new porous PnCs for wider BGs and in-plane mechanical performance. With the aim of PnCs with smooth structural boundaries in the course of the optimization, the floating projection constraints with linear interpolation model are adopted to attain smooth design. The elastic tensor of the structure is solved using homogenization methods, and in-plane mechanical properties are characterized by relevant components, including the bulk modulus and shear modulus reflecting static stiffness, alongside a negative Poisson’s ratio. Some cases are presented, andthe effects of BG order, mechanical properties, volume fraction, and symmetry on bandwidth are discussed, which demonstrates that this method flexibly and precisely achieves inverse and customized multifunctional PnCs design. The effectiveness of the method was further validated by simulation and experiment of mechanical performance. An effective optimization framework for designing multifunctional porous PnCs is proposed, facilitating the integration of different function requirements for practical applications.

中文翻译：

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多功能多孔声子晶体的拓扑优化和定制的面内机械性能


将受生物材料启发的多孔特性整合到声子晶体 （PnC） 结构中可能会带来更广泛的特性或新的功能空间。相反，除了带隙 （BG） 特性外，PnC 中的机械缺陷也对工程应用提出了挑战。因此，这里提出了一种浮动投影拓扑优化 （FPTO） 框架，以设计新的多孔 PnC，以实现更宽的 BG 和面内机械性能。以优化过程中结构边界平滑为目标，采用线性插值模型的浮动投影约束实现平滑设计。使用均质化方法求解结构的弹性张量，面内机械性能由相关分量表征，包括反映静态刚度的体积模量和剪切模量，以及负泊松比。介绍了一些案例，并讨论了 BG 阶次、力学性能、体积分数和对称性对带宽的影响，表明该方法灵活、精确地实现了逆向和定制的多功能 PnCs 设计。通过力学性能的仿真和实验进一步验证了该方法的有效性。该文提出一种用于设计多功能多孔PnCs的有效优化框架，便于集成实际应用中的不同功能需求。