In nonstationary formulation in the context of the classical theories of shells and curvilinear rods we solve the axisymmetric problem of scattering of sound on a spherical shell stiffened by a rib. We analyze the effect of the rib on the spectral density of the echo-signal. We give the results of computing the reflected pulse and classify the sequence of pulses of peripheral waves in the echo-signaLIn recent decades the flow of papers devoted to the analysis of the acoustic fields that arise from the interaction of sound with elastic obstacles has grown steadily (see, for example, the bibliography in [4,5,9]). However due to considerable numerical and mathematical difficulties [9], as of the present it is mainly the acoustic characteristics of simple bodies that have been described. At the same time, as experimental studies have shown [10], even the rotation of a spherical shell about an axis leads to major changes in the picture of the scattering because of its technological inhomogeneity. The introduction of inhomogeneities in the scattering structures, for example, in the form of ribs, separators, or weld seams, causes additional resonances in the scattering amplitude and changes the spatial distribution of the acoustic field, exciting new types of vibrations in the scattering, and so forth [2, I I ].We shall study the properties of an acoustic field scattered by a thin elastic spherical shell stiffened by an elastic rib.Consider a thin elastic spherical shell immersed in an ideal compressible fluid on which a nonstationary plane acoustic wave is incident
pi,c(r, ~, t) = p. f(tl)[H(t~)-H(t t -to) ], t I = t +(rcos~ -a)/c,where p. is a constant having the dimension of pressure, f(t) is the time-modulation of the pulse, H(t) is the Heaviside function, a is the radius of the middle surface, c is the speed of sound in the fluid, t is time, t o is the duration of the pulse, and r, 13, W are the coordinates of a point in a spherical coordinate system with origin at the center of the of symmetry of the shell. Let the shell be stiffened in the middle by a rib rigidly attached to its surface along the circle r = a, ~r = W I. Hence the front of the incident wave will be parallel to the plane of the reinforcement, and the diffraction problem will be axisymmetric. We further assume that the inside of the shell is a vacuum. Here the pressure in the fluid surrounding the object satisfies the relations of linear acoustics and the dynamic equilibrium of the elastic shell-rib system is described by the classical Kirchhoff-Love shell theory and the Kirchhoff--Clebsch theory of curvilinear rods [ 1 ].The problem is to determine the wave field of excess pressure arising in the fluid due to diffraction processes.To obtain the system of equations of the vibrations of this elastic object we apply the HamiltonOstrogradskii principle of stationary action [3]. Then the problem of scattering of sound by a ribbed shell in a fluid can be stated as follows: integrate the system of equations ( / / ,, u+M,2w=O, M2,) M
