Characterizing acceleration spikes due to stiffness changes in nonlinear systems

Abstract Recent studies have reported very large accelerations after stiffness changes in nonlinear systems, particularly self‐centering systems. Some have attributed these accelerations to numerical modelling choices and have assumed that they could be eliminated if the modelling were refined. Others have concluded that self‐centering systems generally have much larger peak accelerations than more traditional systems. This paper demonstrates that accelerations at changes in stiffness are caused by physical phenomena but may be amplified by modelling decisions. This is done by examining the response of a two‐degree‐of‐freedom system after a change in stiffness and by developing a closed‐form mathematical model to characterize this response. The equation shows that acceleration spikes should be expected near small masses and near nonlinear springs that are initially nearly rigid, particularly when those springs change from low stiffness to high stiffness while moving at a high velocity. These acceleration spikes depend on system properties that are often not known precisely, so without physical testing, analytical estimates of the accelerations that occur in nonlinear systems after stiffness changes should be treated with skepticism. Copyright © 2010 John Wiley & Sons, Ltd.