A solution strategy combining the mode superposition method and time integration methods for linear dynamic systems

In this article, the mode superposition method is combined with a time integration method like the trapezoidal rule to improve solution accuracy for linear dynamic systems. In this combination strategy, the essential thing is to decompose a dynamic system into two sub-systems, a small-scale low-frequency system and a high-frequency system. The former can be analytically and efficiently solved with the mode superposition method, and the latter is dealt with through a time integration method such as the Newmark method. The summation of the responses of these two sub-systems is the responses of the original dynamic system. It is concluded that, with little sacrifice of efficiency, the combination method based on the strategy is more accurate than the combined time integration method, but it has the same accuracy order as that of the combined method. Numerical experiments validate the effectiveness of the proposed strategy.