Analysis Of Structural Seismic Response And Damage Based On Chaos Theory

As a kind of time series,ground motion contains rich nonlinear dynamics information,which is the base data in seismic engineering,engineering seismology and engineering seismic design.Traditionally,the ground motion is considered as a random motion,and its research is mainly based on the assumption of smoothness and ergodic assumption,but these two hypotheses have not been proved.With the development of science and technology,researchs on chaos theory in the field of nonlinear science have been widely used,which led to the introduction of chaos theory into seismic engineering and structural engineering.Chaos theory replaces the probabilistic modeling with dynamic modeling,the single variable of the system as the study objects,restoring the motion state of the system by using phase space reconstruction technique and achieving the effect of "from the first small beginnings one can see how things will develop".In this paper,chaos time series analysis is used as the main tool.From the aspect of the duration,the spectrum characteristic,the sampling frequency of ground motion and the self-vibration period,damping of the structure and so on,the chaotic characteristics and studying the damage identification of structural seismic response are analyzed.The main research work accomplished by this paper is as follows:(1)The nonlinear characteristics of time series are analyzed from the perspective of chaos theory.The algorithms for the qualitative and quantitative identification of chaotic characteristics are compiled.The methods are applied to the analysis of the chaotic characteristics of ground motion and the influence factors.The method is also applied to the chaotic characteristics of structural dynamic response.(2)The ground vibrations are analyzed from the perspective of the qualitative and quantitative discriminant index of chaos.The chaotic characteristics of the ground motion are analyzed.The chaotic characteristics of the ground vibration are studied by quantitative index,The influence of the regularity of spectrum,duration,maximum value and frequency of the ground motion are analyzed.The chaotic parameters of the three kinds of vibration,such as ordinary vibration,near-field vibration,far-field harmonic vibration and so on,are calculateed.(3)The chaotic parameters of structural dynamic response under chaotic signal excitation are calculated.The regularity of the change of dynamic response chaotic characteristics by factors such as structural period is revealed.The nonlinear characteristics of structural dynamic response under earthquake action are analyzed.The change rules of the chaotic parameters of the damping,ground vibration amplitude and structure floor are revealed.The changes of the structure response to chaotic characteristics under three kinds of vibration,such as ordinary vibration,near-field vibration,far-field harmonic vibration and so on,are clarified.It is proposed to determine whether the structure enters the clastoplastic stage through the change of chaotic parameters.(4)The damage identification indexes ?D and ?k,based on correlation dimension D and K2 entropy,are proposed.The calculation efficiency of sensitivity,qualitative analysis and damage location of the damage identification indexes are discussed The damage indexes of the single degree of freedom system and the three dimensional and multi-degree-of-freedom structures are analyzed.The relationship between damage states and the damage positions and the damage indexes are established.