Experimental and numerical study of vibro-impact systems with two-sided constraints

Vibro-impact dynamics has been, and still is, the subject of growing interest for its practical and theoretical significance. Many practical engineering problems involve mechanical components or structures repeatedly colliding with one another or with obstacles during their motion. From a theoretical point of view, impact dynamics is highly interesting for the complex nonlinear behaviors and phenomena exhibited by vibro-impact systems, even the simplest. Despite the vibro-impact dynamics has been the subject of intense study, few works deal with the topic resorting to both experimental and numerical analyses. Furthermore, there are still some aspects that, to date, have been little deepened and deserve more attention. The aim of this Ph.D. thesis is to characterize, in a systematic and transversal way, the nonlinear non-smooth response of vibro-impact systems with two-sided constraints. The study was inspired by the practical problem of large horizontal seismic-induced displacements in base-isolated structures. These displacements can damage the isolation system itself or can lead to pounding with surrounding moat walls or adjacent structures if the available seismic gap is not sufficient. The problem was studied considering a single-degree-of-freedom (SDOF) system with two-sided deformable and dissipative constraints (bumpers) under harmonic base excitation and resorting to extensive parametric analyses, of both experimental and numerical nature, continuously interacting and feeding each other throughout the doctoral course. Shaking table tests were carried out on a small-scale physical model, using a rich sensor apparatus, and considering different values of gap amplitude, peak table acceleration and different bumpers. The numerical simulations were performed considering a relatively simple model, in which the impact phenomenon was modeled by a viscoelastic law, and using a Matlab code, specifically created for this purpose. This made it possible to carry out extensive parametric investigations. The adoption of a soft impact model allowed to describe the deformation and the recovery of the bumpers, otherwise not observable by resorting to the coefficient of restitution. The influence of the fundamental parameters which characterize the problem on the system's response was first investigated. The numerical model, despite its relative simplicity, satisfactorily reproduced the experimental results and allowed to extend the range of investigation, compared to the experimental tests. A wide variety of behaviors and phenomena was observed. Different types of primary resonance (without hysteresis, with right or left hysteresis), secondary resonances (without hysteresis, with right or left hysteresis or of non-regular type), non-symmetric responses, multiple impacts, periodic, quasi-periodic and chaotic motion, were highlighted and investigated resorting to different types of representations. The occurrence of the (primary and secondary) grazing phenomenon, and its relationship with some of the observed scenarios, was also highlighted. The transition from a hardening-like to a softening-like behavior was experimentally observed passing from positive to small negative gaps, through the zero-gap configuration. The study of the scenarios, besides being interesting from a theoretical point of view, highlighted possible issues associated with the occurrence of impact. This enabled to make interesting considerations on vibration control. By properly selecting the bumpers' parameters (gap and mechanical properties), it is possible to guide the system's response to reach specific objectives, avoiding some undesirable scenarios and encouraging others, and thus exploiting the occurrence of impact with beneficial effects. Some indications of optimal design of the bumpers are provided to reduce both the displacement and the acceleration of the mass, compared to the case without obstacles, without possibly reducing the vibration isolation frequency range.