Stochastic Seismic Analysis Of Structures Subjected To Near-fault Strong Ground Motions And Chaos Control For Mechanical Systems

The near-fault ground motions have been paid close attention in the community of earthquake engineering and engineering mechanics due to its specific characteristic and seri-ous destroy on structures. In the recent twenty years, the research on engineering properties and structure effects of near-fault ground motion has been an important topic in the field of earthquake engineering. Actually, the selected ground motions are limited by a lack of quali-fied records in database, especially for available near-fault ground motion records. Therefore, the research on the synthesis and simulation of near-fault ground motions has become one of the most important aspects of the performance based seismic design for structures. Moreover, the influence of the orientations of ground motions on structures should not be ignored in the seismic analysis of lifeline engineerings such as large span bridge, pipe laying, dam, etc. In order to better guide the seismic design of critical structures, it is necessary to establish a sto-chastic pulse model that can reflect the ground motions with strongest pulse orientation from the view of a full probability and assess the seismic behavior of high-rise structures subjected to near-fault stochastic strong ground motions.As a specific pseudorandom phenomenon of nonlinear dynamical system, chaos widely exists in the various fields of science and engineering. Recently, chaos control has been an active research topic of nonlinear science, which has been received rapid development and deeply interpenetrated with other branches of disciplines. Meanwhile, chaos feedback control methods have been widely applied to civil engineering and engineering mechanics. Although, these approaches are proposed in distinct application backgrounds at different times, their key ideas are similar. Therefore, some deep investigations on inherent connections between dif-ferent feedback control methods will deepen the comprehension of control strategies, promote the development of other efficient chaos control methods and as well as facilitate their practi-cal application to the mechanical systems. Moreover, the researches on chaos feedback con-trol methods will help achieve the convergence control of structure reliability and probability optimization algorithms.This dissertation performs a systematic and deep study on the dynamical reliability anal-ysis of structure under near-fault stochastic strong ground motions and chaos control in me-chanical systems and the main content are as follows: (1) The power spectral density (PSD) property for near-fault impulsive ground motions is analyzed deeply and the corresponding PSD model based on physical process is derived. A PSD model based on the physical process is proposed to fit the average PSD of near-fault ground motions, and the expression about spectral intensity factor with respect to the seismic source amplitude coefficient, the propagation medium attenuation coefficient and epicentral distance is achieved. Moreover, the reason for the discrepancy of dominant frequency of PSD for near-fault and far-field ground motions is illustrated from a new perspective. A modified piecewise envelope function is established in terms of the properties of pulse-like ground mo-tions with large amplitude and short duration, and the spectral representation method is ap-plied to generate stochastically the samples of non-stationary acceleration time histories with impulsive feature.(2) According to the near-fault ground motions in the orientation of the strongest pulse, a new stochastic pulse model is established, which provides a type of severest ground motions for seismic analysis and design of important structures. The continuous wavelet transform is utilized to obtain the strongest pulse orientation of near-fault pule-like records. The correla-tions between pulse parameters, i.e. seismic moment, rupture distance and site condition and seismological parameters are computed, and a regression model between PGV with strongest pulse and rupture distance is advised. The standard deviations together with those uncorrelat-ed parameters are regarded as random variables, which follow the normal or lognormal dis-tributions well based on the statistical analysis. Then, acceleration time histories of ground motions with high-and low-frequency components are generated by the superposition of the stochastic pulse, and the stochastic high-frequency accelerogram modulated by an intensity envelope function. The synthesized ground motions indicate that the proposed stochastic model can reflect the pulse characteristic of near-fault ground motions.(3) Subset simulation (SS) is applied to compute the dynamical reliability of structures subjected to near-fault stochastic strong ground motions. The influences of variation of sto-chastic pulse model parameters on structural dynamic reliability with different fundamental periods are explored. It is demonstrated that the variation of pulse period, peak ground veloc-ity and pulse waveform number have a significant impact on structure reliability and should not be ignored in reliability analysis. The variations of the other pulse parameters have little influence on structural reliability, and the mean values are just considered in reliability analy-(4) The probability distribution property of chaotic series for Lorenz family chaotic sys-tem is analyzed by probability statistic method. In order to study the probability distribution of chaos series in the neighbour of equilibriums, a hyper-plane containing the equilibriums is established, which reduces the continuous dynamical system to a discrete system. The chaos series of time continuous system correspond to the fixed points of the iterative Poincare map and then the conditional probability distribution of chaos series is obtained. It is indicated that the chaotic orbits are distributed regularly in the phase space of chaotic system, i.e. the fixed points in hyper-plane mainly distribute on both sides of a certain distance from the two sym-metric equilibriums. These points can be adopted as the initial points of some chaos control algorithms to improve the convergent efficiency.(5) The inherent connections among several popular chaos feedback control approaches in mechanical system are revealed, and the stability transformation matrix in stability trans-formation method (STM) is proved to be non-involutory matrix which has more efficiency when applied to stabilize the equilibrium of chaotic system. It is demonstrated that the com-mon global chaos feedback control methods and local chaos feedback control methods based on gradient direction usually involve just one direction vector. However, the stability matrix C of STM contains all the possible search directions, so the above-mentioned several chaos feedback control methods can be regarded as the special cases of S TM. In addition, the S TM can be viewed as a special form of the speed feedback control method (SFCM) when stabiliz-ing equilibriums of continuous autonomous system. Finally, the SFCM is used to stabilize the unstable periodic orbits of continuous non-autonomous system, which indicates that the SFCM can not only stabilize the unstable period orbits of original chaotic system, but also stabilize the original system to the new period orbits that have the similar topological struc-tures to the original ones.