| The frame structure is the most common engineering structure and is widely used in industrial and civil buildings.For the seismic response analysis of frame structures,the damping model is one of the important factors and difficulties which affects the calculation accuracy.In this paper,some model tests are used to investigate the damping model,the identification of physical parameters by the measured dynamic characteristics,and the seismic response calculation of the hysteretic damped system,which are used to improve the calculation accuracy of the seismic response of the frame structure.The main achievements of this dissertation are described as follows:(1)In order to identify the damping ratios of the hysteretic damping structure whose baseline of the measured time history is not strictly zero,a logarithmic decrement method of the hysteretic damped system based on the peak-to-peak value is proposed.On this basis,the free vibration test method with variable balance weights is proposed to research the damping model of the single-story frame structure.The damping model of the frame structure is discussed according to the law of the damping ratio with the change of balance weights.Besides,the least squares identification method is established based on the natural frequencies in different balance weights for the mass and lateral stiffness of the single-story frame.The results show that the damping ratio has nothing to do with the balance weights of the single-story frame,the law of which is the same as the layer-hysteresis damping model.(2)In order to analyze the effect of layer-viscous damping and layerhysteretic damping on the structural modal damping ratio,the research for modal damping ratio of multi-degree-of-freedom concentrated mass shear layer model is carried out,for the flame structure with or without uniform stiffness and mass.The calculation results show that,the layer-hysteretic damping obtain the constant modal damping ratio,which is related to the mass and stiffness distribution of layer-viscous damping;the viscous modal damping ratio increases with the increase of the natural frequency of the structure with uniform stiffness and mass;for structure with abrupt changed stiffness and mass,the damping ratio partially increases with the increase of the natural frequency.On this basis,the experimental modal analysis of 2-story structure,4-story steel structure with uniform vertical stiffness,and 6-story structure with abrupt changed vertical stiffness are carried out.In view of the sparse natural frequencies of the frame structure,a single input and output identification method for dynamic characteristics of multi-degree-of-freedom system with hysteretic damping is established,and the identity of the viscous damping and hysteretic damping identification algorithms for small damping system is certified.The test results show that the vertical mass distribution,stiffness distribution,and natural frequency slight impact the modal damping ratio,and the structure is more in line with the layer-hysteresis damping model.(3)When the modal results are obtained with errors,the mass matrix and stiffness matrix are full matrices identified by modal parameters.However,the mass matrix is a diagonal matrix,and the stiffness matrix is a three-diagonal matrix of the multi-degree-of-freedom concentrated mass shear layer model in theory.To solve this problem,a concentrated mass constraint optimization analysis method and a simplified identification method of stiffness matrix based on the minimum eigenvalue are proposed,which not only meets the characteristics of the physical model,but also has sufficient calculation accuracy.(4)A fast frequency domain algorithm is proposed to solve the problem that the conventional frequency domain algorithm can only obtain the real part solution for the hysteresis damping system.Half of the arbitrary load of Fourier transform sequence are used to construct the discrete sequence of dual loads in this method,then the time history response can be calculated by fast Fourier transform method.Numerical results show that the proposed fast frequency domain algorithm has the same calculation accuracy as the time domain dual load method,and which is higher than the conventional frequency domain method.For modal superposition method of non-proportional hysteresis damping system,the imaginary part response of each generalized coordinate increases with the increase of the damping of the system,and the contribution of the imaginary part is affected by the coupling coefficient,mode parameter coefficient and damping ratio.The errors of real modal forced decoupling method can be limit within 5%when the coupling coefficient is small and the modal damping ratio is less than 5%,otherwise,the imaginary part needs to be considered to ensure the calculation accuracy.(5)A direct integration method with virtual initial condition is proposed to address the instability of the solution of hysteretic damping system.The proposed method develops virtual initial conditions associated to the real initial conditions which makes the direct integration solution eliminating the divergence term of complementary solution and converges to the exact solution.Then,the solutions of central difference virtual initial conditions method were compared with theoretical solutions and frequency domain solutions for the excitations of three different seismic waves in three different natural frequency systems.The results show that the frequency domain analysis results only contain the steady state solutions,which will lead to significant errors in the initial stage of vibration of low natural frequency system;the central differential virtual initial condition method is stable for different conditions,and it will converge to theoretical solution including transient responses.(6)In order to analyze the accuracy of layer-viscous damping and layerhysteretic damping on the seismic response and the rationality of the recognized mass and stiffness matrix,shaking table tests of the 2-story,4-story,and 6-story steel frame models were carried out.Compared with the calculation results,it can be concluded that 1-norm and 2-norm methods may result in significant errors in the structure seismic response for which approximate the structural stiffness matrix from the maximum eigenvalue,so it is not suitable for the inversion of stiffness matrix.The minimum-eigenvalue-based stiffness matrix inversion method shows more accurate calculation results than the inversion method based on the norm,and it is very close to the measured time history.For the damping model,the calculation accuracy and consistency of the layer-hysteretic damping model is generally higher than that of the layer-viscous damping model.Rayleigh damping is an approximate damping matrix,which can also be used to approximate the hysteretic damping system when choosing a suitable two-order reference mode for the Rayleigh damping coefficient. |
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