Research On The Dynamic Characteriscs,Damping Matrix Construction And Seismic Response Of Frame-Type Vertically Mixed Structures

If there are different materials in high direction,the frame structure would be the frametype vertically mixed structure(VMS).Due to the influence of the different damping of the different parts as well as the radiation damping,the VMS is a very complex non-proportional damping system.In this paper,the frame-type VMS is the main object of research.The dynamic characteristics and the physical parameters identification of frame structures are investigated by theoretical analysis and shaking table test.Then,the construction method of damping matrix of the VMS is researched to improve the computational accuracy of the seismic response of vertical hybrid structures.The main research contents of this paper are:(1)To investigate the dynamic characteristics of structures on semi-infinite sites,a random load which is used for the real-time dynamic hybrid test(RTDHT)to modal parameters identification is improved and an associated method of modal parameters identification is proposed.A bandpass stationary random load whose amplitude of the Fourier spectrum is inverse proportion to the frequency is established as the excitation of the real-time dynamic hybrid test.Then,a modal parameters identification technique is developed by the combination of empirical wavelet transform,random decrement technique and the Hilbert transform to obtained the natural frequencies and associated modal damping ratios from the measured vibration responses.Three steel frame structural models are used to modal parameters identification test on the rigid foundation or semi-infinite sites to verify the rationality of the experimental method.(2)A new complex modal analysis method using sequential eigenvalue-shift is developed for the calculation of the modal parameters of the frame structure under SSI effect.This new method is developed based on the understanding that the natural frequencies of the frame structure with consideration of the soil structure interaction are slightly less than that of corresponding fixed-base structure.Accordingly,an index of the local modal mass ratio is proposed to quickly and accurately extract the structural modes from many combinations of modes from structures and soil.(3)To construction the high accracy finite element model of the frame structures test model,based on the natural frequencies and modes obtained from the experimental modal analysis(EMA),an iterative constrained optimization solution by the complete set of measured mode for correcting mass matrix and a least squares solution for the lateral stiffness are proposed.The method takes the total mass of the test model as the constraint condition and develops an iterative correction method for the lumped mass,which is independent of the initial lumped mass.When the measured modes are exact,the iterative solution converges to the exact solution.For the incomplete set of measured mode,a correcting mass matrix method by changing the counterweight is proposed.In the method,the modal experimental results of multiple counterweights are synthesized to directly obtain the lumped mass of the experimental model.On this basis,the weighted least-squares calculation equation of lateral stiffness is established according to the natural frequency and mode.Then,the accuracy and stability of the physical parameter identification method are verified with the numerical model of the 3-story frame structure and the experimental model of the 2-story frame.(4)To construct the damping matrix of the VMS,the experimental modal analysis of a vertically mixed structure with fixed-base or on elastic half space is carried out.On this basis,a Rayleigh damping matrix construction method is proposed,in which the natural vibration frequency of the whole structure is used as the reference frequency for the upper substructure,and the natural vibration frequency of the lower structure is used as the reference frequency for the lower substructure.The modification coefficient of the substructure damping ratio is proposed to improve the construction accuracy of the vertically mixed structure damping matrix under the influence of radiation damping.(5)To consider the influence of radiation damping of soil-structure interaction in the simplified calculation model of vertically mixed structure with fixed-base,The modification coefficient of the substructure damping ratio is used as the reference damping ratio to construct the Rayleigh damping matrix of the substructure.Taking the numerical model of a 10-story vertically mixed structure as an example,the seismic response of the equivalent model with fixed-base is compared with the calculation results of the domain reduction method to verify the rationality and accuracy of the simplified model.(6)Based on the real-mode-based complex mode superposition method,the seismic response analysis of the vertically mixed structure with additional dampers is carried out.The effects of the additional dampers on the modal damping ratio of the VMS are investigated.The calculation error of real mode superposition method with forced decoupling is also reseached.The numerical results show that when the coupling index is greater than 0.2,it is not recommended to analysis the seismic response of the vertically mixed structure by the real mode superposition method using the forced decoupling.