论文标题
基于散射矩阵方法的开放声波指导的拓扑优化
A topology optimization of open acoustic waveguides based on a scattering matrix method
论文作者
论文摘要
这项研究提出了一种拓扑优化方案，用于实现连续体沿开放的声学波导中的结合状态，其中包括周期性的弹性材料。首先，我们使用与波导的单个单位结构相关的散射矩阵来将周期性问题作为线性代数方程的系统。使用边界元素方法在数值上构建散射矩阵。随后，我们采用Sakurai-Sugiura方法来通过解决线性系统的非线性特征值问题来确定谐振频率和Floquet Wavenumbers。我们设计了单位弹性材料的形状和拓扑结构，以使周期结构在给定频率下具有真实的谐振波数，通过最大程度地减少谐振波数的假想部分。提出的拓扑优化方案基于具有新型拓扑衍生物的级别方法。我们演示了提出的拓扑优化的数值示例，并表明它通过一些数值实验实现了连续体中的界面状态。
This study presents a topology optimization scheme for realizing a bound state in the continuum along an open acoustic waveguide comprising a periodic array of elastic materials. First, we formulate the periodic problem as a system of linear algebraic equations using a scattering matrix associated with a single unit structure of the waveguide. The scattering matrix is numerically constructed using the boundary element method. Subsequently, we employ the Sakurai--Sugiura method to determine resonant frequencies and the Floquet wavenumbers by solving a nonlinear eigenvalue problem for the linear system. We design the shape and topology of the unit elastic material such that the periodic structure has a real resonant wavenumber at a given frequency by minimizing the imaginary part of the resonant wavenumber. The proposed topology optimization scheme is based on a level-set method with a novel topological derivative. We demonstrate a numerical example of the proposed topology optimization and show that it realizes a bound state in the continuum through some numerical experiments.
