Interference of Impulses, Scattered and Radiated by Bodies of Spheroidal Form

For ideal prolate spheroids, imitating the school, are calculated the interference of scattered impulses, but for elastic spheroidal shells – the interference of radiated impulses (with the help of the dynamic theory of the elasticity, characteristics of the scattering of the stationary sound and the reciprocity theorem). By the scattering of sound by bodies of the spheroidal form had devoted works [1 – 8], by experiments – [9, 10].


Introduction
For ideal prolate spheroids, imitating the school, are calculated the interference of scattered impulses, but for elastic spheroidal shells -the interference of radiated impulses (with the help of the dynamic theory of the elasticity, characteristics of the scattering of the stationary sound and the reciprocity theorem). By the scattering of sound by bodies of the spheroidal form had devoted works [1 -8], by experiments - [9,10].

Interference of Impulses, Scattered by the School
The interference of impulses with the harmonic filling, reflected by the school, are learnt In [11]. In this paper we will study signals in the form of impulses with the harmonic or frequen-cy -modulated filling. At first we consider the school from three fishes, approximated by three soft prolate spheroids (see Fig. 1), illuminated impulses with the harmonic or frequency -modulated filling. The distance between scatterers are chosen with the help of calculations, fulfilled in [12]. In the process of calculations are found time responses and moduluses of spect-rums of scattered impulses of separate scatterers and the summarized reflected impulse. The angle of the illumination 0 θ was taken three values: 30 , 60 , 90 . S πν has the appearance [13]: where T -the period of oscillations with the frequency 0

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Interference of Impulses, Scattered and Radiated by Bodies of Spheroidal Form  In the frequency -modulated impulse 0 ( ) t Ψ the frequency is changed at the linear depen-dence: where: 6 1, 626 10 a = ⋅ The spectrum 01 (2 ) S πν of the frequency -modulated impulse is determined at the formula: The impulse of the illumination with the frequency -modulated filling 0 ( ) t Ψ and the modulus his spectrum 0 ( ) S ν are represented at Fig. 3.
For the determination of spectrums    The comparison of Fig. 5 and 7 demonstrates, what impulses with harmonic filling more stable to the interference, that impulses with the frequency -modulated filling.

The Interference of Radiated Impulses
At Fig. 8 is represented the plan of the disposition of two elastic prolate spheroidal shells, exciting in points 1 A and 2 A by impulses with harmonic ( Fig. 2) and frequency -modulated (Fig. 3) fillings, the disposition of points 1 A and 2 A corresponds by the spheroidal angle 0 0 θ =  (the axis -symmetrical problem) This problem was decided in [14 -16], we take advantage of this solution. Let us consider a scatterer in the form of an isotropic spheroidal shell, illuminating along axis of the rotation of the shell (the axis -symmetrical problem). All the potentials, including the plane wave potential 0 Φ , the scattered wave potential 1 Φ , the scalar shell potential 2 Φ , the component A ϕ of the vector A  potential and the potential 3 Φ of the gas filling the shell, can be expanded in spheroidal wave functions [14 -16]: The corresponding expressions for the boundary conditions have in the form [14 -16]: Λ is the bulk compression coefficient of the gas filling the shell.
The substitution of series (6) -(10) in boundary conditions (11) -(15) yields an infinite system of equations for determining the desired coefficients. The infinite system is solved by the truncation method. The number of retained terms of expansions (6) -(10) is the greater, the greater the wave size for the given potential.
At the Fig. 9 are represented responses of shells an exciting impulses with the frequency -modulated filling (a) and the harmonic filling (b), but at The presence in the summarized impulse of the impulse with the harmonic filling smoothes over the negative action of the interference at the summarized impulse. Interference of Impulses, Scattered and Radiated by Bodies of Spheroidal Form modulated filling) with Fig. 13 and 14 (the harmonic filling).
The advantage of the application of impulses with the harmonic filling by the interference appears evidently. Figure 11. Responses of three spheroidal shells at exciting impulses with the frequency -modu-lated filling

Conclusions
In the paper were calculated scattered and radiated impulses with harmonic and frequency -modulated fillings for ideal and elastic spheroidal bodies. Signals with the harmonic filling appear more stable to the interference. The study of the interference of impulses, scattered and radiated by bodies of the spheroidal form appears by the object of the research in the hydroacoustic.

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Interference of Impulses, Scattered and Radiated by Bodies of Spheroidal Form