Study On Methods For Non-linear Compound Stochastic Vibration And Their Applications In Engineering

The main effort of this paper is taking some researches on the response of non-linear stochastic structures under non-stationary stochastic earthquake, that is to say, the stochastic response of non-linear compound stochastic vibration system (CSVS)。Based on the publications about CSVS from home and abroad, combinated improved perturbation method to solve non-linear stochastic structures with pseudo excitation method, the improved perturbation pseudo excitation method to solve nonlinear CSVS system of SDOF(single degree of freedom) has been formed. When applying pseudo excitation method, the pseudo response has been expressed in figures. In order to analyze the response of CSVS of SDOF, the researches as follow have been taken: the linear CSVS has been solved by perturbation pseudo excitation method(PPEM) which has been corrected according to independence between space random field and time random progress; as to the nonlinear CSVS, it has been performed by equivalent stochastic linear method and improved PPEM,which is based on linear CSVS. At last, the process of Monte Carlo (MC) method for simulating nonlinear CSVS has been presented.For CSVS of linear MDOF(multi degree of freedom), it has been proposed that the method of direct modal perturbation (DMP) based on selecting point by number-theoretic method(NTM), the DMP method based on selecting point by MC and time history processing analysis(THPA) based on selecting point by NTM to solve its stochastic response. As known that the method of modal superstition (MMS) can be to find srochastic response, here DMP can be uses to find stochastic mode. The researches about this part are as follow:The DMP method has been used to find complex modes of determined dynamical system with damping. As shown in the computational results, the concept of DMP method is much clearer,and it's time-saving and more accurate. When applying the method to MMS, the computational results are also very accurate. Because the damping of civil engineering structures is usually very small, DMP method is appropriate to find the complex modes of the structures. DMP based on selecting point by NTM or based on selecting point by MC have been proposed to find the stochastic modes of stochastic structures. These two methods can be used to solve stochastic modes of un-damping stochastic structures or damping stochastic structures. Firstly, the structures sampling can be formed by selecting point by NTM or MC method. And then, DMP method can be used to calculate stochastic perturbation value of stochastic structure to mean structure. Finally, the stochastic modes can be found by statistic method. When stochastic structures relies on few stochastic variables or stochastic variables with small coefficients of variation, DMP method based on selecting point by NTM would be more efficient than DMP method based on selecting point by MC and more quickly and accurately to find the computational results.In order to find stochastic response of CSVS, the DMP method based on selecting point by NTM, the DMP method based on selecting point by MC and the method of THPA based on selecting point by NTM have been proposed. The computational results of the FOSS method based on selecting point by MC, and the method of THPA based on selecting point by MC have been compared. When stochastic structures relies on few stochastic variables or stochastic variables with small coefficients of variation,stochastic response of CSVS can be quickly and accurately found by the DMP method based on selecting point by NTM, and the method of THPA based on selecting point by NTM.According to the research about linear CSV, it is naturally to apply the DMP method based on selecting point by NTM, the DMP method based on selecting point by MC and the method of THPA based on selecting point by NTM to solve stochastic seismic response of nonlinear soil with CSVS. The relative function method has been applied to solve fluctuating factor of real soil layer random field and the stochastic finite method applied for discreted random field. Stationary stochastic earthquake has been expressed in linear combination between independent stochastic variable and determined process of Karhunen-Loeve expansion based on Hartley orthogonal basic function. Based on work of these preparations, the equivalent linear method and the methods above have been used to find seismic response of nonlinear stochastic soil layer under non-stationary stochastic earthquake. At last, the MC method,PPEM, and the frequency transfer function perturbation method have been used to analyze the effect of structural random damping onstructural displacement.