Discrete continuous mathematical models in the dynamics of horizontal vibrations of buildings

Abstract

In the design practice of design, dynamic models are used, based on the discretization of structures whose inertial parameters are always distributed. The use of discretized models leads to the formation of large-dimensional problems, and the estimation of discretization errors is extremely complicated by the presence of constructive irregularities and heterogeneities of the boundary conditions of the calculated objects. In view of the foregoing, the proposed work is devoted to the formation of mathematical models that allow combining elements with concentrated inertial parameters (discrete elements) with deformable elements whose inertial parameters are distributed (continuous elements). The need for the formation of such models arises, for example, when calculating buildings for horizontal dynamic effects and also when solving the problems of dynamic analysis of building structures with the presence of vibroactive technological equipment.