Modal Parameter Identification And Corresponding Eigenvalue Calculation Of Gravity Dam Based On Seismic Response Data

The eigenvalue(natural frequency)and eigenvector(mode shape)are collectively referred as the eigenvalue problem,which can reflect the natural characteristics of the structure.It's also the main parameters of structure dynamic characteristics,the key to calculate the dynamic response of dam with the mode superposition method and important basis to verify the rationality of the finite element model.Because the measured seismic records is the dynamic response of gravity dam in the working state and the dynamic characteristics of gravity dam could be truly refected by the modal parameters identified with the seismic response.Therefore,it is significant to establish the finite element model of water-dam-foundation with eigenvalue,which is corresponding to modal identification,according to the gravity dam modal parameters identified with the seismic records.The main work and conclusions are as follows:(1)The significance of eigenvalue and eigenvector in analyzing the dynamic problem of gravity dam and several common methods for obtaining the dynamic characteristics parameters are introduced in detail.According to the environmental characteristics of the engineering structure,several modal identification methods applied maturely without the input excitation signal are summarized.In addition,the actuality of modal identification for hydraulic structures is elaborated and the problems of solving the eigenvalue of gravity dam with the FEM are pointed out.(2)The recognition principle of peak method is introduced detailly,this method is improved by introducing the cross power spectral and an identification method which can identif-y the mode coefficients is obtained.The correctness of the theory and program of the improved power spectrum peak method are verified by numerical examples,it demonstrate that this method can be used to identify the modal parameters of the structure only using the vibration response.(3)Several time-domain methods,the natural excitation technology(NExT),eigensystem realization algorithm(ERA),stochastic subspace identification(SSI)and ITD method,are discussed in detail.NExT+ERA of join algorithm and SSI+ITD of the improved join algorithm are proposed based on the characteristics of above methods.The computational efficiency can be improved by the SSI+ITD method,which maintains the recognition accuracy of the SSI method.In addition,the determination of model order problem is solved by the singular entropy increment technique.Numerical example shows that the model order can be effectively identified with the singular entropy increment technique.Meanwhile,NExT+ERA method,SSI method and SSI+ITD method have strong anti-noise ability,such that the signal preprocessing can be avoided.(4)According to the characteristics of water-dam-foundation interaction,the Visco elastic artificial boundary based on the Goodman element without thickness,the process of added water mass calculation and the direct filtering method of solving the eigenvalue problem of gravity dam are introduced on the basis of the free vibration equation.The 3D finite element program DYCDAM.F solving the eigenvalue problem of gravity dam is compiled by FORTRAN and used in Shuikou gravity dam.(5)Based on the measured seismic response of Shuikou gravity dam,the 3D finite element model of gravity dam with corresponding eigenvalues is established by the characteristic frequencies and mode shapes using the spectral analysis,the power spectrum peak method,NExT+ERA method,SSI method and SSI+ITD method.Research show that the calculated characteristic frequency and mode shapes of the model considering the axial elastic foundation is in accordance with the modal identification without considering the foundation quality.The dynamic characteristics of gravity dam under earthquake could be reflected in the finite element model.What's more,the conclusion that the actual elastic modulus of Shuikou gravity dam is higher than the design value could be drawn by the variation of characteristic frequency with the elastic modulus of dam.At the same time,it can be seen that there is a corresponding relationship between mass foundation mode and massless foundation mode in their characteristic frequency based on the discussion results of the model considering the axial elastic foundation.