Exploit the study of the scenarios for the control of the response of single-degree-of-freedom systems with bumpers

In earthquake-prone areas, seismic isolation systems are designed to preserve structural safety and prevent occupants’ injury and properties’ damage. However, seismically isolated structures can be subject to large displacements relative to the ground under earthquakes, which lead to define two problems, the first problem concerns to excessive displacements, whereas the second problem relates to excessive accelerations that occur when the displacements are limited by an obstacle with high relative stiffness. An arrangement that favors the solution of these problems is an appropriate interposition between the isolated structure and the obstacle of the shock absorbers or bumpers. The aim of this paper is to investigate, via numerical parametric analyses, the possibility to exploit the occurrence of impact in a two-sided vibro-impact isolated single-degree-of-freedom (SDOF) system under harmonic base excitation with beneficial effects. Through the analysis of the response scenarios which can occur varying the obstacles’ parameters, that is the width of the gap and the mechanical (stiffness and damping) properties, the target is to reduce both the maximum value of the displacement and of the acceleration of the mass, compared to the free flight condition, without possibly reducing the vibration isolation frequency range. This research path leads to the definition of vibro-impacting control systems and to the free and constrained single and multi-objective optimal design of the control system consisting of the integrated assembly of the isolation system, bumpers and gaps. The main results obtained consist in having (i) found a unique optimality condition, (ii) calculated the dissipated energy and given an energetic interpretation to the optimality condition (iii) built maps, that allow to advance behavior predictions, provide indications on the design and allow to make evaluations of the performance of the vibro-impacting system as a function of the stiffness and damping parameters and of the width of the gap. The stiffness ratio and the damping ratio, which define the mechanical properties of the bumpers, are such that the dimensionless relaxation time is about 1, (iv) finally the results are compared to multi-objective optimal design. Ultimately, the advantages of this new isolation system are: (1) provide a physical limit switch to the isolation system in order to limit the maximum displacement of the mass; (2) reduce the effects of amplification dynamics in the resonance zone; (3) reduce the static displacement, all without possibly modifying the dynamic response in the isolation zone.