Acoustic Analysis of a Finite Cylindrical Shell in an Acoustic Half-Space Based on Fourier Transform Technique

Abstract

In marine and ocean engineering area, some underwater cylindrical shell structures or vehicles may approach a free surface (water surface) or a rigid wall (seabed). The existence of the free surface or rigid wall makes the surrounding fluid around the structure an acoustic half-space, causing that the vibroacoustic characteristics of the shell may have much difference from those in an infinite fluid field. In this study, the far-field acoustic radiation of a finite cylindrical shell with an arbitrary, time-harmonic surface velocity distribution positioned within an acoustic semi-space is studied. The Fourier transform method is utilized to express acoustical pressure in the wavenumber domain, and the acoustic boundary effect is considered through the use of the Graf’s addition theorem and the image approach. Then, the relationship between acoustical pressure and the normal velocity on the structure surface is established in the wavenumber domain. Finally, the far-field acoustical pressure could be expressed by the stationary phase method approximately. The accuracy of the present approach is verified by contrast with the boundary element method. It could be observed that there are many similarities between the directivity of the far-field acoustical pressure of the cylindrical shell and the acoustical dipole due to the interference of sound waves. For the case of a rigid wall boundary, a similar interference phenomenon also exists. The present method has the advantages of simpleness and fewer calculations; it can be utilized to rapidly predict the far-field acoustical pressure in an acoustic half-space. Besides, after discussing the multiple scattering effects between the acoustic boundary and the shell, a simpler physical model is successfully put forward to resolve the far-field acoustical pressure of an inclined shell within an acoustic semi-space, assuming that the distance between the shell and the acoustical boundary is larger than a certain value (five-time radiuses in the present study).