Dynamics of high-rise axisymmetric structures

Abstract

The article discusses the natural and forced oscillations of a "high-rise structure - dynamic vibration damper" system, focusing on its dynamic interactions. A mathematical model of this system has been developed, along with a calculation methodology, a numerical implementation algorithm, and a corresponding computer program that utilizes complex arithmetic tools for an accurate description of dynamic processes. Special attention was given to the viscoelastic properties of the structural material. The Boltzmann-Volterra hereditary law was applied to more accurately describe the time-dependent deformation characteristics. A practical example was explored using the high-rise smokestack of the Novo-Angren thermal power plant, which stands at 330 m tall. The natural oscillation frequencies of this structure were determined, and amplitude-frequency characteristics were constructed accounting for the presence of dynamic dampers and various kinematic impacts. During the problem-solving process, an analysis was conducted on how the parameters of both the structure and the effectiveness of the dynamic vibration damper (DVD) influence the system's response. Various combinations of system parameters were examined to identify patterns in changes to the dynamic response. Based on this research, optimal parameters for dynamic damping of oscillations were established for the real structure, leading to effective reductions in oscillation amplitudes and an increase in the reliability of the structure's operation under dynamic influences.