## 1 Introduction  
In recent years, high-speed railway (HSR) has been widely constructed in a lot of countries and HSR has also extensively transported a large amount of passengers and vast amount of goods, which enables the possibility of long-distance fast travelling and fast goods transportation. Meanwhile, as wide use of HSR, the corresponded problems such as vehicle-induced vibration have made the vehicle-rail-viaduct coupling system worse and worse. An in-depth understanding of the vehicle-rail-viaduct coupling system under complex circumstances shall be indispensable for enhancing the quality and long-term service of HSR infrastructure system [1; 2; 3; 4]. For instance, in [3], the power flow method is applied to analyze the dominant vibration frequencies of the rail bridges for structure-born noise; in [4], the acoustic modal contribution analysis is applied to study the structural noise mitigation performance for the box-girder viaduct. In terms of the HSR infrastructure system, various advancements have been developed and also applied in the engineering, such as the China Railway Track System (CRTS) series slabs [5]. In addition to slabs, the fastener serves as an essential component to mitigate the vibration in the rail system. The fastener has several categories depending on various conditions; for instance, the fastener for normal speed railway systems shall differ from those applied for the HSR system. The HSR system has more than 10 kinds of fasteners, which are designed regardless of distinct engineering circumstances. Figure 1 illustrates two kinds of fasteners and their rubber pads. The mechanical properties of the fasteners can largely affect the dynamic responses of the vehicle-rail-viaduct coupling system [5, 6]. In the fastener's system, the stiffness of the fastener rubber pad contributes 94% to the whole stiffness of the fastener's system, and therefore, the stiffness of the fastener rubber pad can be considered as the whole stiffness of the fastener's system [7]. Since the fastener rubber pad is made of rubber, the stiffness has close relation to the temperature [8]. Considering such temperature-dependent phenomena, extensive investigations have been conducted for studying certain effects. [PERSON] et al. [9] studied the temperature-dependent stiffness of the rubber in the dynamic vibration absorber; [PERSON] et al. [10] conducted temperature sweep tests for rubber, and analyzed the temperature-dependent stiffness of rubber material; [PERSON] et al. [11, 12, 13] investigated temperature-dependent stiffness of the fasteners in the subway system, and studied the nonlinear behavior of the temperature dependent stiffness of the fasteners; [PERSON] [14] conducted temperature sweep tests for the fastener rubber pad, and found that at low temperatures, the fastener rubber pad shows low temperature sensitive performance, which further affects the vibration responses of the coupled system. As mentioned above, although certain investigations have been done for the fastener rubber pad--a kind of viscoelastic damping material [15, 16, 17, 18, 19], not too many studies can be found for the temperature dependent effect of the fastener rubber pad to the dynamic responses of the HSR system [16, 17, 18, 19, 20, 21]. For instance, the effect of the rail fastener on the railway vehicle interior noise is investigated in [16], in order to study the temperature dependent stiffness of the fastener rubber pad, which further affects the dynamic responses of the vehicle-rail-viaduct coupling system.