Resonance phenomena in cylindrical shell with a spherical inclusion in the presence of an internal compressible liquid and an external elastic medium

In the present paper a method is proposed to investigate the behaviour of the axisymmetric system consisting of an infinite thin elastic cylindrical shell submerged in an unbounded elastic medium, filled with an ideal compressible liquid and containing a vibrating spherical inclusion, under periodic dynamic action. The goal is the analysis of the so-called “resonance” phenomena; namely: finding conditions for their appearance, and possible control by means of characteristic parameters of the hydroelastic system under consideration. The technique presented in this work was developed during the realization of a project on elaboration of methods of renewal of oil production in foul wells at the Theory of Vibration Department of the S.P. Timoshenko Institute of Mechanics of the Ukrainian Academy of Science. This mathematical technique allows rewriting the general solution of the corresponding mathematical physics equations from one coordinate system to another, so as to get an exact analytical solution (as a Fourier series) of the interaction problem for a collection of rigid and elastic bodies.