Building oscillations based on a plate model
Makhamatali Usarov, Gayratjon T. Ayubov, Giyosiddin Mamatisaev, Bakhodir Normuminov
Abstract
Abstract The paper is devoted to the numerical solution of the problem of transverse oscillations of a multi-storey building within the framework of a continuous plate model under seismic effects. Cantilevers anisotropic plate is proposed as a building dynamic model, the theory of which is developed in the framework of a three-dimensional dynamic theory of elasticity and takes into account not only structural forces and moments but also the bimoments. The proposed plate model of a building allows us to take into account and study all types of different spatial oscillations of the building structure under the impacts different in direction. Formulas are given for the reduced density, elastic moduli, and shear of the plate model of the building. The base acceleration, given in time by a harmonic law, is taken as a seismic impact. The problem is solved by the finite difference method. Examples are considered and numerical results are obtained. Waveform, displacements, and accelerations distribution diagram of multi-storey high-rise buildings under transverse oscillations are plotted.