Mathematical conformity problems in the dynamic modeling of seismic stability structures

Moscow State University of Civil Engineering, Yaroslavskoe shosse, 26, Moscow, 129337, Russia

^* Corresponding author: mcxmgsu@mail.ru

Abstract

The article discusses the problems of field studies and dynamic stability of construction objects at design stage. It highlights the analysis results of various mathematical model approaches for seismic stability of construction structures. The mathematical aspects of their dynamic properties are represented as amplitude-frequency responses and transfer functions. The results of the study as well as the comparative analysis of the mathematical conformity of modeling dynamic properties of a construction object by the Fourier method and the Laplace method are represented. The article considers the uncertainty in the estimates of the dynamic coefficient of structures when using amplitude-frequency response of the object. Furthermore, it is identified that there is a dependence between this coefficient and the instantaneous spectrum of seismic impact when using the Fourier method. The article gives the results of the studies on causes of virtual dependence of the amplitude-frequency response and on the dynamic coefficient from the Fourier transform basis function. The Fourier transform basis function is proved to fall a long way short of the field data and represents itself some abstract description of seismic loads that do not exist in the real nature. The diagrams are given in the article, that proves the comparative estimates of the mathematical conformity and metrological validity of the construction’s dynamic models when using the Fourier method and the Laplace method.od.