Influence of the foundation bed stiffness on the dynamic properties of the building as of a multi-mass cantilever bar

Abstract

Relevance. The study of the interaction of buildings and structures with the base during an earthquake is one of the most important tasks of the theory of earthquake resistance. The response of the structure to seismic impact depends to a large extent on the ratio of the stiffness characteristics of the soil, foundation, and foundation structure. Moreover, taking into account a rather high degree of statistical variability of the characteristics of the soil foundation, it is possible to ensure the required level of safety of a structure only through the use of probabilistic models and a quantitative assessment of the reliability of the construction-base system as a whole. At present, for the calculation of the construction - base system for seismic loads, deterministic discrete models of the finite element method are mainly used. But these models are poorly adapted for probabilistic calculations and require extensive statistical data, which are currently insufficient. Therefore, in problems of reliability assessment, it is advisable to use simplified analytical models, which make it possible to derive the value of the statistical variability of its reaction with relatively small initial information about the system. The aim of the work - based on the well-known solution for the single-mass model to present an analytical solution in the matrix form of the problem of free horizontal vibrations of a multi-mass cantilever rod on the foundation specified by the elastic half-space model. Methods. A study was made of the effect of the compliance of the soil foundation on the frequencies and forms of horizontal vibrations of the structure. A comparison of the results with the calculation performed by the finite element method is given. Results. The obtained solution is intended to conduct a probabilistic calculation of the construction-base system under seismic loads and evaluate its reliability.