Computation of Rayleigh damping coefficients in seismic time-history analysis of spatial structures

In the seismic time-history analysis of spatial structures under one-dimensional and three-dimensional seismic excitation, significant error will be induced under certain seismic records if the Rayleigh damping coefficients are computed by the traditional two reference modes (TRM) method. To solve the problem, with the modal maximum strain energy as weight, a multi-mode based weighted least square (WLS) method is proposed to compute the Rayleigh damping coefficients. A formula for the Rayleigh damping coefficients obtained by the new method is presented. In the case of one-dimensional and three-dimensional seismic excitation, with the seismic responses under benchmark damping ratio, two double layer cylindrical latticed shells are taken as examples respectively to compare the errors of the new method with those of the traditional two reference modes method. The results show that the new method is more reasonable than the traditional TRM method for spatial structures, and it retains the simplicity and convenience of the Rayleigh damping theory.