An effective strategy for time-stepping in dynamic systems with non-viscous damping

This study develops a precise and reliable time-stepping strategy for evaluating the dynamic behavior of systems with non-viscous damping. The m-point interpolation quadrature method is designed to estimate the non-viscous damping force precisely, and the developed method can be applied to any kernel function. Additionally, to achieve reliable and precise dynamic responses, our research introduces a time integration method with three subs-steps, wherein algorithmic parameters are designed to keep some essential numerical properties. This paper gives the mathematical derivation and computational procedure of the three-sub-step method, and it thoroughly examines its numerical characteristics using a non-viscous damping model. Interestingly, through the theoretical analysis, it is evident that the chosen three-sub-step method has consistent stability, manageable dissipation, reliable stability, and excellent low-frequency precision. At the end of this paper, some representative non-viscous damping examples are conducted. Numerical results show that compared to the dynamic analysis strategies based on the currently popular time integration methods, under the same computations, our strategy enjoys superiorities both in stability, accuracy, and dissipation.