Theory Study And Application Of Nonlinear Stochastic Seismic Responses And Filtering Of Structures

Under strongly random exterior excitation, most structures will undergo elastic-plastic stage and show hysteretic characteristics, the vibration of structure expresses nonlinear random feature. Therefore nonlinear model must be utilized in order to describe the behavior of this kind of structure, also the theory and methodologies of nonlinear random vibration are necessary for analyzing their response. Generally speaking, exterior excitations that act on structure such as earthquake and wind wavelet, etc. are Markov procedure. The random response of structure as well as exterior excitations is Markov procedure. These exterior excitations can be treated as Gauss procedure or filtering Gauss procedure. But because of the nonlinearity, the response of structure is not absolute Gauss procedure. Therefore, basic methodologies for stochastic seismic and filtering responses of nonlinear structure are studied, the approximate solution methodologies and their practical applications are investigated in the dissertation employing equivalent linearization and moment equations method based on FPK equations and Ito stochastic differential equations. The research works are mainly concerned with the following aspects:Firstly, the differential expression of bilinear hysteretic is studied and a new differential expression is developed, then they are demonstrated. The equations introduced which in simple form can be utilized easily to code a procedure. On this basis, sectionalized linearization of bilinear hysteretic structural characteristics and bilinear hysteretic filtering of structural system are put forward.Secondly, random vibration and random filtering differential equations of SDOF and MDOF nonlinear structure are established and deduced employing FPK equations and Ito stochastic differential equations.Thirdly, the methodologies of equivalent linearization and moment equations method in the approximate method for random vibration of nonlinear structure are studied. Random seismic responses of civil engineering structure arecalculated by employing stochastic vibration equations and moment equations methods of nonlinear structures established and stochastic equivalent linearization. In this procedure of calculation, differential expression of hysteretic characteristics and seismic excitation are taken into consideration. Through a great deal of calculation and comparison with the results of Monte Carlo and other methodologies, a conclusion can be drawn that the precision in the calculation of equivalent linearization can satisfy the needs of practical civil applications for general engineering structures.Lastly, based on the observed data of the concrete-filled tubular structures under seismic excitation, filtering analysis of SDOF and MDOF is done respectively by the methods of stochastic equivalent linearization and sectionalized linearization introduced by the author. The simplicity and efficiency of the proposed methodologies are demonstrated by the comparison. The research indicates that the random sectionalized linearization methodology introduced by the author is more simple and efficient than stochastic equivalent linearization method, so it is convenient for generalizing. The study reveals that all these two filtering can eliminate noise efficiently, they are reliable in the case that the strength of observed noise and seismic excitation estimated incorrectly in practice.