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The paper is devoted to the study of dissipative properties of inhomogeneous viscoelastic systems of structures with dynamic vibration dampers. A detailed analysis of well-known studies concerning this problem is given. A mathematical model, technique and algorithm for studying the dissipative properties of inhomogeneous viscoelastic systems of high-rise buildings with dynamic vibration dampers are developed in the paper, taking into account the real geometry of structures. The hereditary BoltzmannVolterra theory was used to describe the viscoelastic properties of the damper and springs material. To solve the problem, the finite element method and the Muller method were used. The natural vibration modes of the Novo-Angren TPP smokestack with dynamic vibration dampers were investigated for various damper parameters. The imaginary part of complex eigenfrequency of the system was used as a dissipative index. A number of new mechanical effects were identified. The developed technique can be used to optimize the parameters of a viscoelastic damper for a structure.

Damping of high-rise structure vibrations with viscoelastic dynamic dampers