Исследования математических моделей процессов деформаций зданий и сооружений

Abstract

Purpose. The article is aimed at analyzing changes in the dynamic characteristics of a building and establishing the dependence of shear deformation accelerations on the building's storey to predict the effect of seismic vibrations on the technical condition of the building, taking into account the engineering and geological properties of the foundation. Methodology. A number of instrumental observations using geodetic devices, automated monitoring systems and engineering seismic stations were made to study the issues of assessing changes in the dynamic characteristics of high-rise buildings and structures. To create mathematical models of deformation processes of buildings and structures, the study of interaction of structural elements of the building with the engineering-geological structure of the ground in the upper and lower parts of the megapolis was proposed. Findings. The results on ground shaking intensity acceleration, effective duration, spectral coefficients and periods of spectrum maximum are obtained. The results of measurements of vibrations on different floors of a high-rise building based on instrumental records of seismic station of local and distant earthquake have been obtained. Dependences of accelerations of shear deformations on the floor of the building with regard to engineering-geological properties of the base have been established. Predictive models of deformation processes of the building taking into account dynamic characteristics of ground vibrations and energy class of earth crust movements have been proposed. Originality. The analytical technique of correlation analysis of random variables is proposed, by means of which normally distributed linear and nonlinear processes are studied to create a mathematical model of deformation processes of buildings of different storeys. Practical value. The obtained results of the study of deformation processes of buildings and their structural elements allow to predict the dynamic model of the process of displacements of points of the structure taking into account the dynamic characteristics of ground vibrations and energy class movements of the Earth's crust