Summary
This work studies a computational approach aimed at establishing equivalent dynamical responses within oscillatory impacting systems subject to soft and rigid constraints. The proposed method incorporates an adaptive differential evolution algorithm with the Metropolis criterion to determine the stiffness and damping parameters of the soft constraint for a prescribed coefficient of restitution governing the rigid constraint. This algorithm aims to achieve equal energy dissipation between the two constraints. Upon examining the dynamical responses of the two impact cases, they exhibit nearly identical outcomes in the two-parameter bifurcation diagrams when subjected to a large restitution coefficient. However, discrepancies arise when the restitution coefficient is low. Detailed numerical tests, conducted using the proposed method, demonstrate enhanced effectiveness compared to previous techniques, such as the prediction formulae outlined by Okolewski and Blazejczyk-Okolewska (Chaos, 31:083110, 2021).
