An improved complex multiple-support response spectrum method for the non-classically damped linear system with coupled damping

摘要

An improved complex multiple-support response spectrum (CMSRS) method considering the coupled damping, which is ignored in conventional CMSRS method, is proposed in this article. Due to the nonorthogonality of the damping matrix, the complex mode analysis method is adopted for equation decoupling. Nine new cross-correlation coefficients are introduced into the CMSRS formulae, thus the correlations between the modal responses under different excitations (velocity or acceleration) are comprehensively considered. A typical structure equipped with concentrated or coupled damper is taken as example to illustrate the differences between the conventional and improved CMSRS methods. Numerical results indicate that, for the structure equipped with the concentrated damper, the coupled damping has a minor effect on the dynamic response. However, for the structure equipped with the coupled damper, the relative deviation between the responses calculated by the two methods increases with increasing damping. The maximum relative deviation of displacement even exceeds 20 %. Therefore, it is significant to consider the coupled damping in seismic engineering.