## 1 Introduction  
Over the past decades, base isolation has been demonstrated to be an effective means to protect crucial structures and their contents from the destructive effects of dynamic excitations. The performance of base-isolated structures against near-fault earthquakes characterized by long-duration pulses with peak velocities has been investigated by several researchers [1,2]. Recent research results have shown that near-fault earthquakes characterized by long-duration pulses with peak velocities will result in significant base displacements and inter-story drifts of a seismically isolated structure [3]. [PERSON] and [PERSON] [4] showed that the fling-step effect would mainly excite the first order modal response of the structures with middle and long natural vibration period, and cause the maximum deformation of the structure at the bottom, which would result in the failure mode of the structure. [PERSON] [5] pointed out that isolation bearings will have a large deformation when the base-isolated structures with long natural vibration period are subjected to pulse-type near-fault earthquakes. [PERSON] [6] examined the performance of a base-isolated structure under the action of near-fault earthquakes with fling-step effect. He found that the base displacement of the base-isolated structure exceeded the permissible displacement of the isolation bearings. The base-isolated structure may cause lateral instability, and the fling-step effect is more harmful than the rupture forward directivity for the base-isolated structure. Due to the large isolator displacements, the isolated structure will suffer some serious problems, such as large permanent base displacement, failure of the isolation bearing and overturning of the superstructure [7]. In addition, as a result of large isolator displacements, the size of the isolation device will significantly increase, which may require much larger seismic gaps between buildings or much larger bridge expansion joints. Therefore, these requirements increase the cost of the construction, which contradicts the primary goal of seismic isolation, which is to design structures more efficiently and economically [8]. In order to enhance the performance of the base-isolated structures subjected to pulse-type near-fault excitations, many kinds of control devices have been proposed [9; 10; 11]. Passive supplemental damping devices can reduce the deformations of the isolation bearings during strong ground motions. However, they may also induce large damper forces and result in increased floor accelerations [12]. Furthermore, when the structure is subjected to weak or moderate earthquakes, passive devices may adversely affect the isolation system since the desired isolation characteristics may be different for these earthquakes. Semi-active control is an effective control alternative that regulates the output power of dampers according to current structural responses. Therefore, semi-active control has better adaptability than traditional passive control. Furthermore, semi-active control requires less power compared to active control, which uses powerful actuators to achieve ideal effects. For these reasons, semi-active control devices have been receiving considerable attentions in recent years. [PERSON] and [PERSON] [13] proposed a variable stiffness device that is used in a sliding isolation system to reduce the seismic response of a base-isolated structure, and the effectiveness of the semi-active device was proved by numerical analytical and experimental studies. [PERSON] et al. [14] proposed a super elastic semi-active damping device in a base-isolated structure and its damping performance was thoroughly analyzed and evaluated. [PERSON] and [PERSON] [15] analyzed and evaluated the dynamic response of a seismically isolated benchmark bridge equipped with viscous and variable dampers, and assessed the performance of these dampers.