长波在弯曲管道中的传播——Ⅱ长波在变截面孔洞中传播时匹配方法的应用
Propagation of a Long Wave in a Curved Duct——(Ⅱ) Applications of Matched Expansion Method to Long Wave Propagation through a Hole with Variable Cross Section
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摘要: 以k表示波数,a表示孔洞横截面的特征半径,本文只研究参数ε=ka≤1(即长波)的情况,本文用正则摄动的方法,给出了长波在变截面孔洞中传播时,其复速度势函数渐近展开的一般表达式;论述了长波在两端开口或一端开口一端封闭的变截面孔洞中传播时,如何用匹配方法求得波在洞口反射、散射和辐射的系数;以三个不同的孔洞作为实例,具体说明三维或二维此类问题的求解方法.Abstract: Only the case in which the parameter ε=ka≤1 is considered in this paper, where k is the wave number and a is the characteristic radius of the cross-section of the hole. The general asymptotic expansion of the complex velocity potential of a long wave propagating in the hole with variable cross-section is obtained by regular perturbation: The methods of matched asymptotic expansion are employed to calculate the reflection coefficients, scattering coefficients and radiation coefficients at the open ends of the hole when a long wave propagates through it, which may be open at both ends or only at one end. Three examples of different kinds of holes are given to show the way to solve such two-dimensional or three-dimensional problems.
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[1] 顾圣士,方光熊,长波在弯曲管道中的传播—I变截面弯管中长波传播的基本分析,应用数学和力学,4.1(1983). [2] Lu Ting and J.B.Keller,Radiation from the open and of a cylindrical or conical pipe and scattering from the end of a rod or slab,J.Acoust.Soc.Am.Vol.61,No.6,June(1977). [3] Lesser,M.B.and J.A.Lewis,Applications of matched expansion methods to acousticsⅠ&Ⅱ,J.Acoust.Soc.AM.51,(1972);1664-1669,Am.52,(1972) 1406-1410. -
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