Insight into Newmark time integration parameters in non-linear dynamic problems

Abstract

In this study, we analyze nonlinear dynamic problems with numerical instability using Newmark (beta-2) time integration methods. By performing parameter study of Newmark method, we show that one parameter lead to numerical damping and the other parameter lead to period elongation only. Period elongation, unlike numerical damping, has been undiscovered as a role of stabilization in nonlinear dynamic problems. We validate our argument by numerical experiments including Newmark methods and Bathe’s composite time integration method. We show that cases exist where numerical damping and period elongation have strength at accuracy over each other. This study gives us a motive for a better time integration method in the future, with wider range of characteristic including both period elongation and numerical damping.