Simplified Seismic Response Analysis Method For Structures With Viscous Dampers

Viscous dampers are widely used in practical projects in view of their simplicity of construction,ease of installation and high seismic performance.However,the nonlinear behavior of viscous dampers makes the seismic analysis of the whole structure more complicated.Therefore,the study of seismic analysis method for structure with viscous dampers have great theoretical and practical value for the application of viscous dampers.At present,the seismic response analysis of structure with viscous damper is usually using the precise numerical integration method or the simplified equivalent damping ratio method.The precise numerical integration methods for solving nonlinear problems require iteration with higher computational cost,which is not suitable for engineering projects.The simplified equivalent damping ratio methods are usually established under some assumption,resulting low accuracy.With this respect,both fine and simplified analysis methods for dynamic analysis of structures with viscous damper are proposed in this paper.And seismic analysis of several structures with viscous dampers are carried out to investigate the reliability of the proposed methods.The specific research work and conclusions of this paper are as follows:(1)Two previous simplified analysis methods are studied in terms of their accuracy and convergence.The result indicates that the existing equivalent methods involves certain errors,and the error increases with the decrease of damping exponent,increases with the increase of damping coefficient.The equivalent method based on energy equivalence is more reasonable,with respect to the equivalent method based on energy dissipation capability,(2)A fine analysis method is put forward,based on the Rosenbrock method.The integration process is simplified by introducing the direction-position matrix of the dampers and the Sherman-Morrison inversion theorem,resulting the modified Rosenbrock method.The modified Rosenbrock method is programmed in MATLAB,and its accuracy and stability are studied through numerical simulations.The analysis results show that the fine analysis method improves the computation efficiency without losing the stability and accuracy of the original method and(3)Starting from the basic theory of equivalent linearization method,a simplified method is proposed in which the equivalent damping coefficients are solved by inter-history iteration.The simplified method is programmed in MATLAB,and its accuracy and convergence are studied through numerical simulations.It is found that the method exhibits clear physical meaning,fast convergence speed and high accuracy.