## 1 Introduction  
The transmission tower is an important component of the transmission line, and the power transmission tower-line system is an important lifeline facility. The damage of a power transmission tower-line system may lead to the paralysis of the power grid. With the increasing height of transmission towers and the span of the transmission line, the seismic risk has increased and several failures have been reported during the past decades. During the 1992 Landers earthquake, about 100 transmission lines, and several transmission towers, failed in the city of Los Angeles [1]. In the 1994 Northridge earthquake, a number of transmission towers were destroyed, and the power system was greatly damaged [1]. During the 1995 Kobe earthquake, more than 20 transmission towers were damaged [2]. In the 2008 Wenchuan earthquake, more than 20 towers collapsed and a 220 kV transmission line in Mao County was destroyed [3; 4; 5]. As shown in Figure 1, the 2010 Haiti earthquake caused damage to transmission towers. During the 2013 Lushan earthquake, more than 39 transmission lines were destroyed [6]. Therefore, studies on the vibration control of power transmission towers needs to be conducted to improve and guarantee the safety of transmission lines.  
Some research about the vibration control of a transmission tower under wind loading has been conducted at home and abroad [7; 8; 9; 10; 11; 12]. However, there are few studies about the vibration control of transmission towers under earthquake excitation. In recent years, researchers have conducted studies regarding impact dampers. [PERSON] et al. [13] investigated the performance of impact dampers from free damped vibration generated when a step function input was supplied to a leaf spring with a free mass. [PERSON] [14] studied the vibration control capability of a combined tuned absorber and impact damper under a random excitation using numerical and experimental methods. [PERSON] et al. [15] researched the free vibration of a vibratory system equipped with a resilient impact damper. The results presented above show that the impact damper can reduce the response of structures. Due to space limitations, vibration control devices are not suitable for transmission towers. Therefore, a new type of vibration control device has been developed which combines the impact damper and tuned mass damper (TMD). [PERSON] et al. [16] proposed a new type of TMD, the bounding tuned mass damper (PTMD), to upgrade the seismic resistance performance of a transmission tower. Compared with TMD, the bandwidth vibration suppression of PTMD is larger, so the vibration reduction effect of PTMD is better than that of TMD. The PTMD has also been applied for vibration control of subsea pipeline structures [17; 18; 19] and traffic poles [20], and both simulation results and experimental results have demonstrated the effectiveness of the PTMD. However, in the previous studies, the PTMD has been simulated by a modified Hertz-contact model. Since the Hertz-contact model cannot be established in finite element modelling (FEM) software, such as ABAQUS, the primary structures were all simulated by simplified multi-mass models.  
Based on the above research, two-dimensional vibration controls of a power transmission tower with a PTMD under multi-component seismic excitations are performed. A three-dimensional finite element model is created in ABAQUS according to practical engineering. The vibration reduction mechanism of the PTMD is introduced, and the PTMD is simulated using finite element software. To compare with the vibration reduction effect of the PTMD, the vibration control of the TMD is also conducted. A parametric study of the PTMD is carried out to provide a reference for the optimal design of a transmission tower with a PTMD.