Two time integral algorithms with numerical dissipation and without overshoot for structural dynamic
结构动力响应数值算法耗散和超调特性设计

The seven free parameters were introduced into the governing equation of a motion to design new direct integral algorithms for solving structural dynamics problems. Two new one-step schemes were presented by selecting free parameters in the process of algorithmic finite difference analysis. The proposed methods are implicit, unconditionally stable, second-order accurate, numerically dissipative, and no overshot. One of the algorithms is able to annihilate the high-frequency modes asymptotically, and is more dissipative than Houbolt method for damped system. The numerical dissipation of the other method is minimum in the low-frequency regime and is controllable in the high-frequency regime. An analysis of the overshoot property is directly performed for damped system and show that proposed two algorithms no exhibits overshoot, while the HHT-a scheme suffers from the displacement and velocity overshoot simultaneously when damping existed. Finally, the results of the analysis were validated numerically by the comparison with the Newmark, HHT-a and Houbolt methods by analyzing a simulated two degree-of-freedom system representing a large structural.