Spurious resonances in numerical time integration methods for linear dynamics

This paper deals with the accuracy of time integration methods for linear d ynamics when applied near the resonance condition. An approach for the anal ysis is considered which allows spurious resonance conditions to be detecte d. The analysis of Newmark methods shows the existence of such conditions w hich can adversely affect the quality of numerical computations, As an alte rnative, a higher order algorithm, which can be viewed as a generalization of the trapezoidal rule, is investigated. The analysis reveals that the spu rious disturbance near the resonance condition is greatly reduced. The repo rted numerical tests confirm the theoretical predictions and demonstrate th at high-quality simulations can be obtained by means of higher order algori thms. (C) 2000 Academic Press.