A new method for calculating seismic response of non-proportionally damped structures

For seismic response analysis of structures withnon-proportional damping characteristic, the derived and presentedtraditional calculation methods based on proportional damping will no longerbe accurate in theory, and in some cases even produce incorrect results. Inview of such problems, engineering and academia often adopt the directintegration method for exact solution, which would need relatively largecomputation cost, and the forced decoupling method with high efficiency forapproximate solution which would introduce unknown error. Taking intoaccount the equilibrium of accuracy and efficiency, a new method forcalculating non-proportionally damped structure's seismic response ispresented, which is named as multiple-degree-of-freedom modal equationmethod. The derivation also points out that the direct integration methodand forced decoupling method are two special extreme forms which can beobtained from the proposed method, and thereby the integrated theory systemfor non-proportionally damped structure's seismic response calculation isestablished. Finally, numerical study is carried out to verify theavailability of the proposed method in the calculation of seismic responseof non-proportionally damped structures, and it shows that along with thechanging of dimension number of equation and partitioned mode of structurethe efficiency and accuracy of the proposed method also gradually change andcan be adjusted.