Vibrations of high-rise buildings under seismic impact taking into account physical nonlinearity

Abstract

Analytical description of vibration loads of the complex construction structure is considered as a system of masses connected by means of viscoelastic springs. To take into account the rheological properties of the spring material, the Boltzmann-Volterra principle is used. A mathematical model of the problem under consideration has been developed, which boils down to the solution of a system of nonlinear integro-differential equations. A solution method based on the use of quadrature formulas has been developed and a computer program has been compiled on its basis. The results are shown as graphs. Influence of nonlinear and rheological properties of spring on amplitude and phase of mass oscillations is investigated.