REAL MODE SUPERPOSITION METHOD FOR ANALYSIS OF SEISMIC RESPONSE OF NON-PROPORTIONALLY DAMPED ISOLATED STRUCTURES

An approximate method for analyzing seismic response of non-proportionally damped base isolated structures in time domain is derived by combining real mode superposition and Laplace transform method. The non-proportional damping matrix is expressed in the form of sub structural Rayleigh damping model. Three of the isolated buildings which were designed by the authors have been used as numerical examples, inputting two different earthquake waves under 3 different isolation damping levels. A comparison of calculated results is made with complex modal superposition, the Wilson-θmethod coded in double precision Fortran, and the Simulink method in Matlab. It is shown that under the design damping level defined in this paper, i.e., the isolation damping ratio is 0.21, the result of the present method is basically as accurate as the Wilson-θmethod, and the maximum relative errors of the peak displacement, velocity and acceleration are less than 0.07%, 0.19% and 0.27%, respectively, of their maximum response. Even if under an extremely heavy damping level (isolation damping ratio 0.81), the maximum relative errors of all peak responses of interest are still less than 4%, indicating that the method presented in this paper is sufficiently accurate for use in engineering analysis.