Generalised eigenfunction expansion and singularity expansion methods for canonical time-domain wave scattering problems

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS Wave Motion Pub Date : 2024-10-11 DOI:10.1016/j.wavemoti.2024.103421
Ben Wilks , Michael H. Meylan , Fabien Montiel , Sarah Wakes
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Abstract

The generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the time domain. The GEM, which is shown to be equivalent to d’Alembert’s formula when no scatterer is present, is also derived in the case of a point-mass scatterer coupled to a spring. The discrete GEM, which generalises the discrete Fourier transform, is shown to reduce to matrix multiplication. The SEM, which is derived from the Fourier transform and the residue theorem, is also applied to solve the problem of scattering by the mass–spring system. The GEM and SEM are also used to solve the problem of wave scattering by a mass positioned a fixed distance from an anchor point, which supports more complicated resonant behaviour.
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典型时域波散射问题的广义特征函数展开和奇异性展开方法
应用广义特征函数展开法(GEM)和奇异性展开法(SEM)求解了时域中无限拉伸弦上波散射的典型问题。在没有散射体存在的情况下,GEM 与达朗贝尔公式等价;在点质量散射体与弹簧耦合的情况下,也推导出了 GEM。离散 GEM 是对离散傅立叶变换的概括,证明它可以简化为矩阵乘法。由傅立叶变换和残差定理推导出的 SEM 也被用于解决质量-弹簧系统的散射问题。此外,GEM 和 SEM 还被用于解决与锚点保持固定距离的质量的波散射问题,它支持更复杂的共振行为。
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来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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