Study On Stochastic Response Analysis Method Of Long Span Bridges Under Nonstationary Excitations

In nature,typhoon,downburst,earthquake,wave and other random excitations usually show strong nonstationary characteristics.With the extensive construction of modern large-scale structures,the response of structures under these excitations tends to be nonstationary and nonlinear.Although the theory and method of random vibration analysis of structures have been greatly developed,there are still many constraints on nonstationary and nonlinear analysis of large structures.Among them,the problem of computational efficiency has received more attention in recent years and is also urgent to solve.Therefore,taking the extreme wind and ground motion as examples,the time-varying power spectral density estimation of non-stationary excitation and random simulation are first studied in this dissertation.Then,the frequency domain method for nonstationary random response analysis of linear and nonlinear structures is discussed and studied,and the computational method of random response of long-span bridges under strong winds and ground motions is further studied.The main work and results are as follows:The time-varying power spectral density estimation of non-stationary excitation can not only provide the target spectrum model for the frequency-domain method of structural stochastic response analysis,but also provide the target spectrum model for the sample simulation of time-domain analysis.In order to deepen the understanding of time-varying spectral estimation,this dissertation studies various methods for the time-varying spectral estimation from the perspective of frequency domain,and presents the general form of the spectral estimation formula.Firstly,the unified formula of time-varying spectrum estimation for the overlap and non-overlap band are derived in frequency domain,respectively.Then the performance of various methods and the selection of estimation parameters are studied by estimating the target spectrum.Finally,the time-varying spectrum estimation of the measured wind speed data is carried out,and the accuracy of estimation results is checked by the time edge function and the frequency edge function.Random simulation is the basis of the time domain method of stochastic dynamic response analysis.At present,the spectral representation simulation of multivariate nonstationary processes is still relatively inefficient.In this dissertation,the classical spectral representation simulation method is firstly extended to simulate the multivariate nonstationary stochastic processes with the time-varying coherence,and the fast Fourier transform(FFT)technique is applied to simulate the nonstationary stochastic processes with time-varying coherence.Then,the simulation of time invariant coherent multivariate nonstationary processes is improved from the perspective of proper orthogonal decomposition(POD)and FFT.Finally,for simulating the wind speed field of long-span bridge,an enhanced closed-form solution of Cholesky decomposition is proposed,which can be used for the simulation of stationary or nonstationary wind field along an arbitrary axis.Through the above processing,the two major steps of spectral representation simulation are optimized: Cholesky decomposition of spectral matrix and summation of trigonometric functions,which greatly improves the simulation efficiency and lays a foundation for the efficient time-domain analysis of engineering random vibration.Because of the explicit input-output relationship,the frequency-domain method based on power spectrum density to describe the input-output relationship is widely used in the structural random vibration analysis.However,for large structures,the efficiency of traditional methods based on the pseudo-excitation method and precise-integration method is facing some challenges.Therefore,this dissertation proposes an FFT method to accelerate the time-domain integral calculation involved in the structural nonstationary response analysis.First,the efficiency of the traditional nonstationary random response analysis is discussed.Then,the FFT method for the random response analysis of linear structures under uniformly and generally modulated nonstationary random excitation are proposed,respectively.Then,the method is extended to the nonstationary responses analysis of nonlinear systems by the equivalent linearization method.Finally,it is applied to the analysis of nonstationary buffeting response of long-span bridges.Since the traditional time history analysis at frequency is converted to FFT at time,the computational efficiency is greatly improved.In addition,this method is explicit to time,and the general response statistics are slowly varying with time,so FFT is only needed at a few critical time instants in the linear calculation,and each iteration only needs to calculate the response at a specific time instant in nonlinear calculation.In the nonstationary random response analysis of non-proportionally damped structures with dense modes,the traditional frequency-domain method usually uses the direct integration method to avoid complex modal analysis.Due to the large amount of time history analyses,the computational efficiency is still limited.In order to improve the efficiency of response analysis,this dissertation proposes a fast convolution method based on Duhamel integral.First,two methods are presented to efficiently identify the discrete-time impulse response of a linear structure with respect to excitation.Then FFT is used to quickly calculate the convolution between the excitation and the discrete-time impulse response.Furthermore,based on the equivalent linearization method,the fast convolution method is extended to nonstationary response analysis of nonlinear structures.Finally,based on the fast convolution method,the random response analysis method of long-span bridges under the multi-dimension,multi-support,arbitrarily coherent and completely nonstationary seismic excitation is established.Because time analyses are greatly reduced,FFT is used in the fast convolution method,and it is explicit to structural freedom and time,this method can greatly improve the computational efficiency of nonstationary response analysis.