## 1 Introduction  
Pavement excitation usually affects vehicle performance and passenger ride experiences and even influences the health of drivers and passengers. For instance, the pavement conditions of military vehicles, agricultural vehicles, mining vehicles, and other special vehicles are very poor; the drivers usually drive these vehicles in a harsh environment over a long period, and they are likely to suffer cervical spondylosis, spinal fracture, and other injuries. Therefore, it is important for vehicle vibration reduction designs to cut off the adverse vibration transmissions between pavement and the main system, which aims to offer drivers and passengers a comfortable ride environment [1]. Vibration reduction can be achieved through the vibration transmission path, which is vehicle tires [2], vehicle suspension [3], and vehicle seats [4]. Of these three measures, vehicle suspension is the most frequently adopted measure; by designing different suspension types and operating principles, the vehicle's ride comfort can be improved to different degrees [5]. Vehicle tires are the carrier between the vehicle and the pavement for force transmission; although reducing tires' vertical stiffness and pressure can improve vehicle comfort, this can lead to greater rolling resistance and generate greater friction heat, which, furthermore, shortens the tires' service life [6]. Designing vehicle seat suspension with superior vibration isolation performance is a convenient and direct way to improve passenger comfort, and it has less impact on other vehicle performance parameters [7]. The dynamic vibration absorber (DVA) is another method used in the vehicle vibration area; it reduces the main system vibration with an attached mass-spring-damper device [8]. A hydraulic semi-active DVA was constructed by [PERSON] and [PERSON] for vehicle suspension with the application of the bi-state control algorithm, which enhances the passenger ride experience and vehicle performance [9]. [PERSON] et al. [10] devised two types of DVAs for vehicle seats, which effectively reduced the turbulence of the vehicle seat. [PERSON] et al. [11] proposed an active vehicle suspension with an attached DVA for electric vehicles and decreased the maximum force acting on the in-wheel motor bearing. [PERSON] and [PERSON] [12] presented an active DVA based on the linear quadratic regulation (LQR) control method for vehicle suspension, which enhances the vehicle's dynamic performance. [PERSON] et al. [13] built an electric vehicle in-wheel DVA to weaken motor vibrations. In summary, the DVA has been used in vehicle engineering to reduce vehicle vibration with its simple structure; while the effective vibration suppression bandwidth of a linear DVA is relatively narrow, and its robustness is restricted, the vibration suppression performance of a linear DVA can change a lot when its structural parameters slightly vary. In recent years, as a type of nonlinear DVA, nonlinear energy sinks (NESs) have caused extensive concern and have been deeply studied [14]. A NES mainly has nonlinear stiffness properties; it couples with the main system through nonlinear stiffness and linear damping, which absorb and dissipate the energy that passes one way from the main system to itself. By attaching a NES, the main system can have less vibration amplitude and a wider vibration suppression bandwidth than a linear DVA; NESs have been applied in mechanical engineering [15; 16], civil engineering [17; 18], and aerospace engineering [19; 20] because of its advantages. One primary goal in the vehicle design stage is meeting the lightweight design criteria, which can reduce fuel consumption per one hundred kilometers, increase vehicle mileage, and maintain vehicle durability and safety. A NES can reduce the main system's vibration effectively at the expense of a relatively large mass, which is against the goal of lightweight vehicle design.