The acoustical problem dealing with the interaction of a plane wave propagating along the liquid-filled cylindrical cavity with an elastic spherical shell filled, in turn, with the compressible liquid is solved. An axisymmetric case is studied. The boundary problem for simultaneous solution of the wave equations describing the motion in the fluid filling the vessel as well as in the fluid contained within the shell together with equations of motion of the thin elastic shell is formulated. The problem statement contains the boundary conditions for both fluid–shell interfaces, the condition at the vessel surface and far-field radiation conditions. The incident wave propagating along the vessel axis is expanded into a normal mode series. In order to meet all boundary conditions, the variable separation method along with the spherical wave function representations in terms of the cylindrical ones and vice versa are used. This approach yields exact solution of the boundary problem and enables one to analyze the scattered fields in the low and medium frequency ranges. The problem is reduced to an infinite system of algebraic equations that is solved by the truncation method. The goal of the study is to determine the interaction features between the shell and the vessel surfaces. Obtained numerical results describe scattered field of pressure and velocity in the neighborhood of the shell as functions of frequency, the internal liquid characteristics, and the elastic characteristics of the shell. It is ascertained, that peculiarities of the resonance behavior of the liquid-filled shell can be essentially amplified by the acoustical interaction with the vessel surface.

解决了平面波沿充满液体的圆柱腔传播与弹性球壳之间的相互作用的声学问题，而弹性球壳又充满了可压缩液体。研究了一个轴对称情况。描述了填充容器的流体以及壳内流体中的运动的波动方程的同时求解边界问题以及薄弹性壳的运动方程。问题陈述包含流体-壳界面的边界条件、容器表面的条件和远场辐射条件。沿血管轴传播的入射波被扩展为正常模式系列。为了满足所有边界条件，使用变量分离方法以及圆柱体方面的球面波函数表示法，反之亦然。这种方法产生边界问题的精确解，并使人们能够分析低频和中频范围内的散射场。该问题被简化为通过截断方法求解的无限代数方程组。该研究的目标是确定外壳和容器表面之间的相互作用特征。获得的数值结果将壳附近的压力和速度散射场描述为频率、内部液体特性和壳的弹性特性的函数。据确定，