Pipe vibration attenuation through internal damping and optimal design of vibro-impact systems.

Pipelines periodically supported by rack structures (PPRs) are common in chemical and petrochemical plants, among others, and conventional tools such as dampers and hysteretic absorbers are commonly used to mitigate large vibrations in these systems. In this study, we explore two alternative strategies: (i) enhancing the attenuation rate of PPR vibrations through structural internal damping, and (ii) using nonlinear vibro-impact systems (VIS) to reduce seismic vibrations in a PPR. To shed light on the first strategy, we develop analytical dispersion relations for a PPR and show how damping can improve the mitigation capabilities of the periodic system. As for the second strategy, we consider a 9-node beam, i.e., a single span (SS) of a PPR equipped with a VIS, and combine the central composite design (CCD) and Kriging metamodelling to maximize dissipation energy and minimize the number of impacts. This multi-objective optimization problem aims to find the most effective design solution for the VIS in terms of gap and coefficient of restitution (COR). Additionally, we consider the stochastic nature of seismic input and the possible chaotic behavior of the VIS. To account for the sensitive variability of the number of impacts in seismic records, we perform incremental dynamic analyses and calculate fragility functions for various engineering demand parameters, including the number of impacts. We define a 3D surface for selecting the optimal gap-COR pair. When impacts occur, transient results can be chaotic, and we compute the largest Lyapunov exponents of a few representative trajectories.