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.

Dynamic behavior of a high-rise structure is investigated in the paper taking into account linear and nonlinear strain and energy dissipation caused by internal friction in the building material under various kinematic effects. An algorithm and program have been developed for the dynamic calculation of high-rise axisymmetric structures under various dynamic effects. Unsteady oscillations of the high-rise axisymmetric structure represented by a one-dimensional model - a viscoelastic beam of the annular cross-section with a variable tilt of the generatrix and a variable thickness are considered. Dynamic behavior of a high-rise structure in the resonant mode under short-term pulsed effect, under prolonged pulsed effect, under the sinusoidal-damped effect, under real seismic impact is studied and the graphs of displacement changes over time of various points of the structures are plotted. It was found that the dynamic response of a high-rise structure is affected not only by the magnitude of the dynamic load but also by its frequency spectrum and duration. Under the impact of a frequency close to the natural vibration frequency of the structure, significant displacements occur, and, if the material does not possess dissipative properties, the structure could collapse, being in the resonant mode.

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