Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123, Trento, Italy.
IGF - Ingenieurgesellschaft Dr. Ing. Fischbach mbH, An Der Vogelrute 2, 50374, Erftstadt-Lechenich, Germany.
Sci Rep. 2023 Apr 20;13(1):6510. doi: 10.1038/s41598-023-33640-y.
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.
管架周期支撑管道（PPRs）在化工和石化等工厂中很常见，通常使用阻尼器和迟滞吸收器等传统工具来减轻这些系统中的大幅振动。在本研究中，我们探索了两种替代策略：（i）通过结构内阻尼来提高 PPR 振动的衰减率，以及（ii）使用非线性振动冲击系统（VIS）来降低 PPR 中的地震振动。为了阐明第一种策略，我们为 PPR 开发了分析色散关系，并展示了阻尼如何提高周期性系统的缓解能力。至于第二种策略，我们考虑了一个 9 节点梁，即 PPR 的一个单跨（SS）配备了一个 VIS，并结合中心复合设计（CCD）和克里金元模型来最大化耗散能量并最小化冲击次数。这个多目标优化问题旨在为 VIS 在间隙和恢复系数（COR）方面找到最有效的设计解决方案。此外，我们考虑了地震输入的随机性和 VIS 可能的混沌行为。为了考虑到地震记录中冲击次数的敏感变化，我们进行了增量动力分析，并为各种工程需求参数计算了易损性函数，包括冲击次数。我们定义了一个用于选择最佳间隙-COR 对的 3D 曲面。当发生冲击时，瞬态结果可能是混沌的，我们计算了几个代表性轨迹的最大李雅普诺夫指数。
