Application of fractional order operators to the simulation of ducts with acoustic black hole terminations
Application of fractional order operators to the simulation of ducts with acoustic black hole terminations
复制标题
DOI：
10.1016/j.jsv.2019.115035
复制
发表时间：
2020-01
影响因子：
4.7
通讯作者：
John P. Hollkamp;F. Semperlotti
中科院分区：
文献类型：
--
作者：
John P. Hollkamp;F. Semperlotti
我们调查的分数阶运营商的潜力，以开发准确和有效的模型声学黑洞（ABH）的终端管道。虽然以前的研究已经成功地开发了方法来估计ABH终端的反射系数，ABH元素在较大的结构部件和组件的集成往往导致计算密集型模型。模型的大小通常由空间离散化要求驱动，空间离散化要求是捕获实现ABH效应所需的幂律几何变化所必需的。在努力探索建模方法，可以导致大量的嵌入式ABH的结构的有效模拟，我们开发的一维分数阶模型能够仿真的ABH终止在声管道中的吸收行为。两种建模方法将讨论基于分数阶边界条件或分数阶声学域的ABH终止。在其最一般的形式，我们的方法合成积分微分模型的基础上运营商具有复值，分数和频率依赖的顺序。这些模型的作用和影响的ABH元素模拟结构的研究和比较，从传统的建模技术的结果，以评估ABH系统的分数阶建模的可行性。
We investigate the potential of fractional order operators to develop accurate and efficient models for acoustic black hole (ABH) terminations in ducts. While previous research has successfully developed methodologies to estimate the reflection coefficient of ABH terminations, the integration of ABH elements in larger structural components and assemblies often results in computationally intensive models. The size of the model is typically driven by spatial discretization requirements necessary to capture the power-law geometric variation required to achieve the ABH effect. In an effort to explore modeling approaches that could lead to effective simulations of structures with large numbers of embedded ABHs, we develop one-dimensional fractional order models capable of emulating the absorbing behavior of an ABH termination in an acoustic duct. Two modeling approaches will be discussed based either on a fractional-order boundary condition or on a fractional-order acoustic domain of an ABH termination. In its most general form, our methodology synthesizes integro-differential models based on operators having complex-valued, fractional, and frequency-dependent order. The role and implications of these models for simulating structures with ABH elements are investigated and compared with the results from traditional modeling techniques in order to assess the viability of fractional order modeling for ABH systems.