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

For seismic response analysis of structures with non-proportional damping characteristic, the derived and presented traditional calculation methods based on proportional damping will no longer be accurate in theory, and in some cases even produce incorrect results. In view of such problems, engineering and academia often adopt the direct integration method for exact solution, which would need relatively large computation cost, and the forced decoupling method with high efficiency for approximate solution which would introduce unknown error. Taking into account the equilibrium of accuracy and efficiency, a new method for calculating non-proportionally damped structure's seismic response is presented, which is named as multiple-degree-of-freedom modal equation method. The derivation also points out that the direct integration method and forced decoupling method are two special extreme forms which can be obtained from the proposed method, and thereby the integrated theory system for non-proportionally damped structure's seismic response calculation is established. Finally, numerical study is carried out to verify the availability of the proposed method in the calculation of seismic response of non-proportionally damped structures, and it shows that along with the changing of dimension number of equation and partitioned mode of structure the efficiency and accuracy of the proposed method also gradually change and can be adjusted.