Nonlinear dynamic response of the vibro-impact systems subjected to harmonic ground motion under conditions of uncertainty on the gap size

In isolated structures, the large relative displacements with respect to the base that occur as a result of significant seismic actions can excessively deform and damage the isolation system or can lead to pounding with adjacent structures if the distance between the structures (gap) is not sufficiently large; this can result in local or structural damage and damage to equipment contained in the structure due to increased absolute accelerations. One way to mitigate this damage is to insert appropriate deformable and dissipative devices (bumpers) between adjacent structures. The objective of the work is to evaluate, by numerical analysis, how uncertainties on the gap parameter, initially assumed to be symmetrical and positive, can give rise to nonsymmetrical and negative gaps and can also significantly influence the nonlinear dynamic response of a vibro-impact single-degree-of-freedom system optimally designed and excited with harmonic excitation at the base. The main results obtained showed how the presence of an uncertainty in the gap, modeled through normal probability distributions, is reflected i) on the nonlinear dynamic response of the system with values that lie in frequency-dependent confidence zones, (ii) on the probability distributions of the response quantities (the absolute accelerations and relative displacements of the mass and the deformations and forces in the bumpers), (iii) on the width of the intervals in which the probability distributions of the response turns out to be of normal distributions, (iv) on the link between the gap values and the values obtained from the different response quantities considered.