Spurious resonances in numerical time integration methods for linear dynamics

This paper deals with the accuracy of time integration methods for linear dynamics when applied near the resonance condition. An approach for the analysis is considered which allows spurious resonance conditions to be detected. The analysis of Newmark methods shows the existence of such conditions which can adversely affect the quality of numerical computations, As an alternative, a higher order algorithm, which can be viewed as a generalization of the trapezoidal rule, is investigated. The analysis reveals that the spurious disturbance near the resonance condition is greatly reduced. The reported numerical tests confirm the theoretical predictions and demonstrate that high-quality simulations can be obtained by means of higher order algorithms.