## 1 Introduction  
Piping systems are crucial to the functionality of commercial and industrial buildings including offices, shopping malls, hospitals, airports, and plants. The building piping systems consist of water/gas pipes, ventilation, and cable conduits, which are mounted on overhead slabs. However,considering the significance to the operation of the building, the seismic safety of piping systems has not received the attention it deserves. As a nonstructural component, piping systems are usually based on empirical design and thus their design does not take potentially large deformations (e.g., which may occur during an earthquake) into account. To date, there is no specific seismic design code for bearing capacity including piping dynamic deformation. Thus, seismic safety of piping systems is a noteworthy issue. The historical earthquake disaster loss survey shows that the consequences of piping system damages are multifaceted [1,2]. First, piping systems are important nonstructural components in buildings, and consist of a considerable proportion of the total building investment [3,4]. Damage to piping systems can therefore potentially result in drastic economic consequences. Second, the destruction of a piping system can cause serious secondary disasters including flooding. Both in the Hawaii earthquake (2006) [5] and the Chile earthquake (2010) [6], severe water damage occurred subsequently to piping system damage. Furthermore, the destruction of the piping system can cause the failure of function, which is unacceptable for key infrastructures including hospitals, airports, water supply companies, and fire extinguisher systems. The 1994 Northridge earthquake was a convincing example. After the earthquake, hundreds of patients had to be evacuated due to the disrupted functionality of 13 hospitals [7]. More than 100 fires were ignited and were not extinguished in time due to the destruction of fire protection systems [8]. In the San Fernando Valley, 80,000 to 100,000 people were out of water for five days due to over 3000 leaks in the water supply piping system [9]. The disaster loss investigation reports indicate that suspended piping systems with high flexibility have the most serious seismic damage [7]. In practical engineering, there are two types of suspended piping systems: one is suspended by single rods at intervals (as shown in Figure 1a), the other one is supported by trapeze hangers (as shown in Figure 1b). Both types of piping system possess high mechanical flexibility, which can lead to large deformation (i.e., strain) due to seismic loadings. The direct consequence of large deformation is structural damage caused by the collision of the piping system with adjacent components or equipment [10]. In addition, differential deformation and stress concentration are other damage types that can occur in the piping system [10]. Thus, reducing the seismic responses of the piping system can greatly improve the safety of the entire building system. In new buildings, seismic braces are added to limit the deformation of the piping system. The seismic braces secure the piping system at the price of having the piping systems possibly enduring large internal forces [11,12]. However, for existing buildings, the overhead space can be filled with various equipment and facilities, which can complicate the installation of seismic braces within the limited space. Compared to seismic braces, passive dampers have the distinct advantage of reducing the vibration motions of piping system to an acceptable range. Passive dampers are widely used in the vibration control of industrial piping systems in a variety of complex environments. Figure 1: Two types of suspended piping systems: (**a**) A single rod piping system; (**b**) trapeze hangers supporting a suspended piping system. In the Arctic Circle, tuned mass dampers (TMDs) were applied to mitigate wind-induced vibration of approximately 30,000 spans of pipelines.