Abstract
A mathematical model and a technique for assessing the efficiency of the dissipative ability of structurally inhomogeneous mechanical systems consisting of multilayer cylinders bonded to a thin viscoelastic shell of finite length have been developed. A detailed analysis of the known works devoted to this problem is given. A model, methodology, and algorithm for studying the natural and forced oscillations of a system to assess the damping ability of structurally inhomogeneous elastic and viscoelastic mechanical systems, taking into account the influence of the geometric and physico-mechanical parameters of the shell and cylinderhave been developed. In solving the problems considered, the method of divided variables, the method of the theory of potential functions, the Mueller method, the Gauss method and the orthogonal sweep method were used. The complex eigenfrequencies, amplitudes of forced oscillations are determined, and the largest dephasing abilities of the considered structurally inhomogeneous systems are estimated. It has been revealed that, the effect of the greatest damping ability in structurally heterogeneous systems is manifested when the real parts of complex natural frequencies come closer due to the interaction of close natural forms with each other.
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