Novel Criterion for Evaluation of Stationarity in Nonlinear Structural Dynamics

Abstract

The evaluation of stationarity, such as the widely used steady-state response assessment in stepped-sine testing, is a critical issue in structural dynamics. Stepped-sine excitation is a crucial testing method for nonlinear structures. This method can provide high signal-to-noise measurement data but requires a long measurement time. The disadvantage of lengthy measurements stems mainly from the prolonged time for a structure to reach a steady-state response in each frequency step. Although stepped-sine testing has been applied in numerous studies, there is still no uniform criterion to exactly indicate the moment when the response of a testing structure begins to achieve a steady state. In this study, a precise and novel criterion for evaluating stationarity in nonlinear structural dynamics based on the trend of the squared 2-norm of sinusoidal fitting residual vectors is proposed. Three numerical examples show that the steady-state response determined periodically by the criterion is in good agreement with the results of the theoretical analysis, which demonstrates that the presented criterion not only can assist engineers and researchers in accurately checking steady-state response but also can reduce the unnecessary and redundant waiting time during stepped-sine testing; therefore, the comprehensive performance of stepped-sine testing applied in nonlinear structures can be improved.