论文标题
波导中的空间瞬态行为,具有损耗的阻抗边界条件
Spatial transient behavior in waveguides with lossy impedance boundary conditions
论文作者
论文摘要
具有损失阻抗边界条件的声学波导中的衰减与非热和非正常算子有关。该主题已在基本和工程研究中进行了广泛的研究,传统上认为,可以通过单独考虑每个横向模式的衰减来完全捕获总声音的衰减行为。在这种情况下,经典工具之一是Cremer最佳概念,旨在最大程度地减少衰减模式的衰减。但是,典型的声场可能是多种横向模式的叠加,这些模式是非正交的,并且单个模式衰减可能与总声音衰减无关。通过使用奇异值分解,我们将衰减最小的总声幂与非正态传播器的最大奇异值联系起来。最小衰减的总声音的行为仅取决于有损边界条件和频率,但与来源无关。对于任何有损阻抗边界条件,尽管所有模式都呈指数型减弱,因此声音几乎沿波导过渡区域几乎是未偿还的。如果阻抗接近传播器的特殊点,则该空间瞬态显得特别强烈,在该点上,一对相邻模式可以实现Cremer最佳概念预测的最大衰减。这些结果是使用非模式数值计算和两乘玩具模型确认的。
Attenuation in acoustic waveguides with lossy impedance boundary conditions are associated with non-Hermitian and non-normal operators. This subject has been extensively studied in fundamental and engineering research, and it has been traditionally assumed that the attenuation behavior of total sound power can be totally captured by considering the decay of each transverse mode individually. One of the classical tools in this context is the Cremer optimum concept that aims to maximize the attenuation of the least attenuated mode. However, a typical sound field may be a superposition of a large number of transverse modes which are nonorthogonal, and the individual mode attenuation may have little to do with the total sound power attenuation. By using singular value decomposition, we link the least attenuated total sound power to the maximum singular value of the non-normal propagator. The behaviors of the least attenuated total sound power depend only on the lossy boundary conditions and frequency, but are independent of sources. The sound may be almost non-decaying along the waveguide transition region for any lossy impedance boundary conditions although all modes attenuate exponentially. This spatial transient appears particularly strongly if the impedance is close to an exceptional point of the propagator, at which a pair of adjacent modes achieve maximum attenuation predicted by Cremer optimum concept. These results are confirmed using non-modal numerical calculations and a two-by-two toy model.