Study On Random Dynamic Response Analysis Method And Application For Long-Span Bridges Subjected To Non-Stationary Excitations

Excitations in nature such as wind, wave and earthquake exist randomness. With the development of modern structures toward long-span and high-rise, and the wide use of high-strength materials, the non-stationarity, non-linearity and non-Gaussianity of random excitations and structural responses have become important factors in refined structural design and they also draw much attention from the engineering community. In recent years, the research work related to non-stationarity has been made great achievements, but there are still some problems need to solve. The non-synoptic winds and earthquake ground motions will be taken as examples to study non-stationarity of the excitations and their effect on structures in this paper. On the one hand, the non-stationarity decriptions of random excitations in time-frequency domain, the evolutionary power spectral density (EPSD) estimation and random simulation are discussed in detail. On the other hand, the theory methods to predict the random dynamic responses of a long-span bridge and the influence of non-stationarity on structural responses are systematically studied. The main work and conclusions are as follows.In engineering practice, the number of measured non-stationary samples is limited (often only one available sample). A new adaptive time-frequency analysis framework for multivariate non-stationary signals based on multivariate empirical mode decomposition (MEMD) is established through a qualitative perspective. The scalogram and coscalogram, and instantaneous frequency spectra and cospectra are proposed to represent the transient characteristic of a multivariate non-stationary signal. The framework provides a complement analysis method for multivariate non-stationary signals, which can not be performed by both EMD and EEMD. The effectiveness of the proposed MEMD-based time-frequency analysis framework is demonstrated by numerical examples of a thunderstorm downburst and an earthquake ground motion.How to estimate the EPSD of non-stationary random excitation is well discussed by a quantitative perspective. The results show that the Priestley method has advantage for a single sample, and the wavelet transform method performs a high precision for multiple samples. A set of seismic samples from three directions are also used to reveal EPSDs and time-varying coherence function among different directions. Furthermore, the consistent non-stationary features can be observed from both qualitative analysis and quantitative analysis.Numerical simulation of non-stationary samples is a prerequisite to carry out structural dynamic response analysis in time domain. However, in classical simulations of multivariate fully non-stationary processes, the decomposition efficiency of EPSD matrix is low due to the inseparability of frequency and temporal variables. A novel Cholesky decomposition method and interpolation techniques are proposed in a stochastic simulation method which is capable of generating spectrum-compatible ground motion samples.Take full-scale downburst winds as examples, an empirical formula for determining the maximum frequency in time-varying mean is recommended and how to extract time-varying mean from original wind speed sample is discussed. The features of wind-induced transient dynamic responses of high-rise buildings are summarized. The results show that DWT with higher orders of Daubechies wavelet and EEMD have good performance in deriving the mean wind speed of downbursts, and should be recommended. Also, it is noted that maximum value of the structural response calculated by non-stationary analysis is slightly delayed with respect to time at which the quasi-static response reaches its maximum.An efficient scheme based on pseudo excitation method is established to predict non-stationary wind-induced buffeting random response of a linear time-varying (LTV) wind-bridge system, and the scheme is then applied to investigate the buffeting performance of a steel-box girder suspension bridge in the mountain area. The results show that a uniformly modulated non-stationary EPSD model is appropriate to represent non-stationary fluctuations. The time-dependent nature of mean wind and wind fluctuation results in lower response compared to quasi-static and steady states. Traditional stationary treatment (original wind speed is represented by 10 min constant mean plus stationary wind fluctuation) may underestimate the buffeting responses, which indicates that it is appropriate to model non-stationary wind speed as the summation of a time-varying mean and a stationary/non-stationary fluctuation.Also with a long-span suspension bridge as an example, a unified framework to analyze transient seismic response of multi-degree structures subjected to multi-dimension and multi-support non-stationary evolutionary excitations is presented based on pseudo excitation method and improved complex Cotes precise integration method. This framework can guarantee the calculation accuracy, and is convenient to consider the spatial effects and the correlation among different components of tri-dimensional earthquake ground motions. The results show that the smaller damping and natural frequency of a long-span structure which result in more significant transient effect caused by non-stationary earthquake ground motions, and the response values of the suspension bridge analyzed by intensity non-stationary model is larger than those by fully non-stationary model.It is found in this study that the non-stationarities of wind speeds have significant variation of intensity and weak variation of frequency content, whereas earthquake ground motions are non-stationary in both intensity and frequency. In order to comprehensively discuss the two types of non-stationarities, thus non-stationary wind speeds and earthquake ground motions are taken as examples to illustrate in this paper.