UNDERWATER OBJECT CLASSIFICATION BY MEANS OF AN ACOUSTIC METHOD EUGENIUSZ KOZACZKA

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1 UNDERWATER OBJECT CLASSIFICATION BY MEANS OF AN ACOUSTIC METHOD EUGENIUSZ KOZACZKA Naval Uiversity of Gdyia Gdyia, Śmidowicza 69, Polad Gdańsk Uiversity of Techology 8-95 Gdańsk, Narutowicza 11/1, Polad The paper deal with the basic problem coected with the free vibratio of fiite cylidrical steel shell immersed i water. At the first there is described the theoretical model of this problem by meas of the Helmholtz equatio with the vo Neuma boudary coditio o the radiated surface. Next the results of a umerical ivestigatio are preseted. The fial results are the acoustic characteristics obtaied i the sea. These oes were compared to the umerical results.. INTRODUCTION Uderwater object detectio, idetificatio ad classificatio immersed or buried by meas of a acoustic method has bee of great iterest for a few decades by acousticias maries ad archaeologists. There are ofte used the objects e.g. mies, amphoras i a fiite cylidrical shape or similar. The method of active locatios (echolocatios) is very popular i detectio of the immersed or buried objects. I the shape of reflected soudig pulse oe ca observe the rigded part of soudig pulse ad so-called tail. I this tail we ca fid a substatial feature of the object, that scattered the soud pulse. This paper described the basic method that allows to determie the shape, volume of the cylidrical steel shell immersed or buried i the sea. 1. PROBLEM FORMULATION For describig the pressure distributio i a far field we used the Helmholtz equatio i the followig form: r r r Φ R) + k Φ( R) = f ( ) (1) (

2 1 1 = ( q ) + q q q q q = z + y, R = ϕ q + x + x, The solutio of this equatio is as follow: r Φ( r ) Φ( R) = r G( R, r N S G( R, r is a radiated surface ad ) is a Gree fuctio. S ) ds () O the source surface for r = a should be satisfied the boudary coditio so-called vo Neuma coditio i this form: Φ( r ) r r = w& ( ) (3) N r = a w& ( r ) is ormal velocity of the shell vibratio. The pressure distributio is described by the followig formulae: acρ iπ / ( + 1) i( ωt kr) p = W& m me e [ J ( kasi Θ) + ie ( kasi Θ)] ψ (4) 4R si( kl / cos Θ) ( kl cos Θ) ψ = [1 + ] cos Θ (mπ ) ( kl cos Θ) c - speed of soud; ρ - medium desity; J ( ), E ( ) - Bessel ad Weber-Lommel fuctios order respectively. Geometric cofiguratio of radiatig cylider is preseted o figure 1.

3 Fig. 1. Geometric cofiguratio of radiatig cylider We assume that cylidrical surface is covered by cotiuous distributio of sigle sources give by: r Wm mπ w& m ( ) = & [1 cos (x + L)] cos ϕ (5) L m, are modal ad odal umber respectively, is amplitude of ormal velocity. W& m Aother relatio is obtaied whe we take ito accout the pressure wave radiatio by a part of a ifiite cylider. It is give by these formulae: ixξ = iρωm iϕ A ( ξ, ϕ ) H ( τr) e p e π d τh τa ξ m (6) ( ) ξ is a wave umber i x directio. After simplificatio we obtai: cρε ( ) iπ / i( ω t kr) p = W& ψ m m me e 4πkR (si Θ) H ( ka si Θ) (7) ε ( ) = 1 for = ε ( ) = for 1 Distributio of soud pressure ca be fid by meas of the relatio (4) or (7) for the cases whe we kow ω ad coected with them W &. O the figure the chart of p m ad p m as fuctio of kasi Θ was preseted. m m 1

4 Fig.. The chart of p ad m 1 p as fuctio of kasi Θ m To ormalized these fuctio we divided it by factor: acρ W& m ϕ. (8) 4R. EXPERIMANTAL INVESTIGATION As a first step we are carried out examiatios of the ormal velocity distributio o the cylidrical steel shell. The cylidrical shell was immersed i water i a aechoic basi. O its surface was mouted velocity trasducer as is show i figure 3. Fig. 3. Positio of mouted velocity trasducer at cylidrical shell These sigals after a pulse excitatio were recorded ad aalysed. O the base of this examiatio we ca estimate fudametal frequecies coected with free oscillatios frequecies. Figure below show a example of velocity sigal observed at poit VIII.

5 Fig. 4. Sigals observed at poit VIII O the figure 5 are show the form of fuctio for differet free vibratios frequeces. The velocity distributio alog the x - axis ad ϕ - agle. Fig. 5. The forms of fuctio for differet free vibratio frequeces

6 3. MEASUREMENTS CARRIED OUT IN THE SEA The ext step of these ivestigatios were measuremets of scattered soud pressure by a fiite cylidrical steel shell excitig by soud pulse geerated by the impulsive source. This kid of source allows to excite low free oscillatios of the cylidrical shell for e.g. less tha f = Hz. I figure 6 are show two curves as a results of compariso of two differet relatios betwee the values obtaied by meas of theoretical relatio ad measuremet oe. The better approximatio gives the relatio (7). Fig. 6. Results of compariso of two differet relatios 4. CONCLUSIONS Fidig a free oscillatio of a immersed fiite cylidrical steel shell we ca estimate its volume ad shape ad some times also iside cotet. These ivestigatios are a first step to fid a method for iterpretatios some relatio betwee geometrical relatio of the target ad scattered soud field. The ext step of the ivestigatio will be devoted to the proper sigal processig allowig to extract the iterestig iformatio from scattered sigal. REFERENCES [1] Proceedigs of The applicatio of recet advaces i uderwater.detectio ad survey techiques to uderwater archeology, Bodrum, May 4. [] A. Kołodziejski, E. Kozaczka, Broadbad source of uderwater disturbaces, Archives of Acoustics 1,,, 197-1, 1986

METHOD OF FUNDAMENTAL SOLUTIONS FOR HELMHOLTZ EIGENVALUE PROBLEMS IN ELLIPTICAL DOMAINS

METHOD OF FUNDAMENTAL SOLUTIONS FOR HELMHOLTZ EIGENVALUE PROBLEMS IN ELLIPTICAL DOMAINS Please cite this article as: Staisław Kula, Method of fudametal solutios for Helmholtz eigevalue problems i elliptical domais, Scietific Research of the Istitute of Mathematics ad Computer Sciece, 009,