波系在液体中的弹性管梁上的反射和辐射

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Reflection and Radiation of a Wave System at the Open End of a Submerged Elastic Pipe

摘要: 本文研究入射波系在液体中的半无限弹性管梁的开口端的反射和辐射问题,此波系由管梁上的挠曲波和管内、管外液体中相应的表面波(声波)所组成.利用Fourier变换,将这个半无限问题严格地归结为求解Wiener-Hopf型方程.然后将液体和管梁的密度比作为小参数,用摄动法求近似解.文章着重研究了反射系数的计算,还给出了远场的辐射型式曲线.

Abstract: The reflection and radiation of a wave system at the open end of a submerged semi-infinite elastic pipe are studied. This wave system consists of a flexural wave in the pipe, an acoustic surface wave in the fluid exterior to the pipe and an acoustic wave in the pipe's interior. Fourier transform techniques are used to formulate this semi-infinite geometry problem rigorously as a Wiener-Hopf type equation. An approximate solution is obtained by using a perturbation method in which the ratio of the massdensities of the fluid and the pipe material is regarded as a small parameter. The calculation of the reflection coefficient is emphasized, and the polar plots of the radiation coefficient are also presented.

[1]	Helmholtz,H.,Theorie der Luftschwingungen in Röhren mit offenen Enden,Crelle's J.Reine Angewandete Math.,57(1860),1-72.
[2]	Rayleigh,Lord,Theory of Sound,Vol.2,Dover(1945),196-201,487-491.
[3]	Levine,H.and J.Schwinger,On the radiation of sound from an unflanged circular pipe,Phys.Rev.,73(1948),383-406.
[4]	Vainstein,L.,The theory of sound waves in open tubes,Zh.Tech.Fiz.,19(1949),911-930.
[5]	Jones,D.S.,The scattering of a scalar wave by a semi-infinite rod of circular cross section,Phil.Trans.Roy.Soc.,A247(1955),499-528.
[6]	Williams,W.E.,Diffraction by a cylinder of finite length,Proc.Camb.Phil.Soc.,52(1956),322-335.
[7]	Song,J.,A.N.Norris and J.D.Achenbach,Acoustic radiation generated by local excitation of submerged beams and strings,J.Sound Vib.,100(1985),108-121.
[8]	Kornecki,A.,A note on beam-type vibrations of circular cylindrical shells,J.Sound Vib.,14(1971),1-6.
[9]	Graff K.F.,Wave Motion in Elastic Solids,Ohio State Univ.Press(1975),154-155.