Practical performance of the \(\theta _ 1\)-method and comparison with other dissipative algorithms in structural dynamics (Q1090157)

A single-step time marching scheme, the \(\theta _ 1\)-method, is presented. The method leads to an unconditionally stable implicit algorithm with controllable numerical dissipation. A comparison with other known dissipative algorithms is made. The accuracy, the spectral properties, and the overshooting behaviour are investigated. Numerical results for linear single and multi-degree of freedom systems are presented. Among the class of unconditionally stable implicit algorithms with numerical dissipation the \(\theta _ 1\)-method shows some advantages over other known methods, especially in accuracy and over- shooting behaviour. The computational effort for nonlinear problems is comparable to Newmark's trapezoidal rule.