Research On Higher-order Analysis Of Linear Structure Random Vibration Under Non-gaussian Excitation And Dynamic Reliability

Various uncertainties often exist in nature,and the various loads that engineering structures are subjected to during service are usually characterized by stochastic processes,such as wind gusts,earthquakes,waves,and pedestrian loads.The accurate evaluation of the response of a structure under random loads is an important part of random vibration analysis and an important basis for structural dynamic reliability analysis.Although the analysis theories and methods for random vibration analysis of linear structures have been widely employed,the computational efficiency,computational accuracy and applicability of random vibration analysis under non-Gaussian excitation are still affected by many limitations.Therefore,how to perform random vibration analysis under non-Gaussian excitation efficiently and accurately is an important problem in the field of random vibration.Therefore,in this paper,the study of random vibrations with non-Gaussian excitation is carried out first.Then,the higher-order moment spectrum model of nonGaussian stochastic processes is investigated.Finally,the structural dynamic reliability study is carried out for the non-Gaussian random vibration analysis.For the random vibration under single-point non-stationary non-Gaussian excitation,an efficient and accurate higher-order analysis method is proposed based on the pseudoexcitation method.Firstly,according to the definition of higher-order moment spectrum of non-Gaussian stochastic process,the relationship between the higher-order moment spectrum model of uniformly modulated non-Gaussian random process and the higherorder moment spectrum model of stationary non-Gaussian random process is established.Secondly,according to the mode superposition method,the expressions of time-varying higher-order moment spectrum of structural response under single-point uniformly modulated non-Gaussian excitation are derived.Then,the higher-order pseudo-excitation method is employed to obtain the higher-order pseudo-response and the higher-order moment spectrum expression of the response.Finally,the higher-order virtual response is calculated by the time-domain explicit method,and then the higher-order analysis method of random vibration under single-point non-stationary non-Gaussian excitation is proposed.Under the theoretical framework of the pseudo-excitation method,the multipoint correlated Gaussian excitation is transformed into multipoint independent Gaussian excitation by the moment spectrum matrix decomposition of the excitation.For the multipoint correlated non-Gaussian random excitation,it is difficult for the existing theoretical analysis methods to decompose multipoint correlated non-Gaussian random excitation into independent non-Gaussian random excitation by the high-dimensional moment spectrum matrix decomposition of multi-point non-Gaussian excitation.In order to implement the random vibration analysis under multiple non-Gaussian excitation,it is necessary to propose a new method that does not involve the decomposition of the second-order moment spectrum matrix,and extend it to the random vibration analysis under multiple non-Gaussian excitation.An auxiliary harmonic excitation generalization method,which can avoid truncated degree of mode and power spectrum matrix decomposition,is proposed for random vibration analysis with second-order moment spectrum,i.e.,random vibration analysis under Gaussian excitation.Firstly,the concepts of generalized impulse response function,generalized frequency response function and generalized evolving frequency response function are proposed by considering the effects of the action position and vibration type of random loads,and the generalized analysis method which is equivalent to the complete quadratic term combination method is deduced.Then,the auxiliary harmonic excitation generalized method is proposed by combining the generalized analysis method,in which the product of the generalized frequency response function is substituted by the product of the response of the auxiliary simple harmonic excitation.Finally,according to the different ways of solving the response of the structure under the auxiliary harmonic excitation,two schemes of the auxiliary harmonic excitation generalized method are proposed,namely,the auxiliary harmonic excitation generalized method based on the mode superposition method and the auxiliary harmonic excitation generalized method based on the time domain analysis.Following the idea of the auxiliary harmonic excitation generalized method,a higher-order analysis method for the random vibration of linear structures under multiple non-Gaussian excitation is proposed.Firstly,the relationship between the higher-order moment spectrum model of multiple uniformly modulated non-Gaussian random process and the higher-order moment spectrum model of multiple stationary h non-Gaussian random process is established.Secondly,by introducing the generalized time-varying impulse response function and the generalized time-varying frequency response function and combining with the vibration superposition method,the higher-order moment spectrum expressions of the response under multiple non-Gaussian excitation are derived.Then,the computational expressions of the higher-order moment spectrum of the response are reconstructed by the response of the auxiliary harmonic excitation and the higher-order moment spectrum of the multiple non-Gaussian excitation with the idea of auxiliary harmonic excitation generalized method.Finally,an efficient higher-order analysis method for the response analysis of linear structures under multiple nonGaussian excitation is proposed based on the time-domain explicit method.In order to promote the wide application of higher-order analysis methods in stochastic vibration,the calculation methods of higher-order moment spectrum models for specific non-Gaussian random processes commonly found in engineering structures are proposed and applied to random vibration analysis because the research of the higherorder moment spectrum models for non-Gaussian random processes is quite uncommon.Firstly,for the first type of specific non-Gaussian stochastic process,i.e.,square Gaussian stochastic process,the higher-order moment function of the square Gaussian stochastic process is derived through the higher-order moment function of the Gaussian stochastic process,and then the higher-order moment spectrum of the square Gaussian stochastic process is obtained by combining the multiple Fourier transform.Then,for the second type of specific non-Gaussian stochastic process,i.e.,the non-Gaussian stochastic process with known first third-order statistical moments,the second-order moment spectrum of the corresponding Gaussian excitation is obtained by the second-order Hermite moment model and the third-order statistical moments of the non-Gaussian excitation,and then the higher-order moment spectrum of the non-Gaussian stochastic process is determined by combining the higher-order moment spectrum of the squared Gaussian stochastic process.Finally,the higher-order analysis of the linear structure random vibration under a specific non-Gaussian excitation is carried out.Combining the results of linear structural random vibration analysis under nonGaussian excitation,a widely applied structural dynamic reliability analysis method is proposed.Firstly,for the stationary non-Gaussian stochastic response process,the probability density function of the response is approximated by the normal inverse Gaussian distribution,and then the dynamic reliability of the response is calculated by the Poisson distribution assumption.Then,for the non-stationary non-Gaussian stochastic response process,the joint density solution method of the response is proposed by combining Gaussian Copula function and Mehler’s formula,and the dynamic reliability analysis of the structural response is proposed.