# Dynamic Characteristics of the Bouc-Wen Nonlinear Isolation System
## 1 Introduction  
In recent years, the idea of seismic isolation building is widely used in civil engineering, vehicle engineering, aerospace engineering and other fields, such as the construction of commercial complexes, hospitals, residential buildings, tunnels and subway stations, shock absorption of vehicles and launch of rockets, etc. This is achieved mainly through the installation of seismic energy-absorption devices or coating with damping materials to achieve the optimal application of different material characteristics, which can ensure that the isolation system effectively protect the superstructure from earthquake damage or damage. At present, with the continuous development of seismic isolation technology, countries around the world are also carrying out research on seismic isolation theoretical systems related to seismic isolation structures [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. As one of the most important parts of the isolation structure, the mechanical properties of the isolation layer are mainly hysteretic characteristics; meanwhile, the hysteretic nonlinearity system usually is a kind of multi-valued, non-analytical system, so it is very difficult to establish a mathematical model of the universal hysteretic nonlinear system. In previous works, [PERSON] used a bilinear hysteretic model to study the random vibration of the system [15], and some scholars also used a piecewise linear hysteretic model to analyze the system response [16]. However, in the piecewise linear model, due to the abrupt change in stiffness, it is difficult to reflect the yield characteristics of the system. For this reason, relevant scholars began to use the smooth curve model to analyze a hysteretic system [17]. In 1967, [PERSON] proposed a simple and smooth hysteretic model controlled by differential equations. Later, [PERSON] et al. improved this model and proved that this model could generate a series of different hysteretic loops [18]. Subsequently, the Bouc-Wen model was developed as a smooth curve hysteresis model, which includes both nonlinear stiffness and damping; it can approximate all kinds of smooth hysteretic curves and reflect the mechanical properties of the system under different control parameters well. Therefore, the model has been widely used in research and analysis in the field of engineering applications. Domestic and foreign scholars have also made relevant explorations regarding the solving methods of nonlinear systems. For example, [PERSON] used the stochastic parameter analysis method to describe the response of the seismic isolation bridge model and evaluated the performance of the seismic isolation device [19]. [PERSON] used Incremental Dynamic Analysis (IDA) to determine the response of analyzing the nonlinear model [20]. [PERSON] adopted the state space method to analyze the Hysteretic Energy Sink [21]. [PERSON] used a numerical simulation method to mainly analyze the parameter characteristics of a nonlinear hysteretic system [22]. [PERSON] adopted the normalized Bouc-Wen model to describe the hysteretic characteristics of a magnetorheological damper [23]. [PERSON] analyzed the asymmetric hysteresis behavior of the Bouc-Wen model based on phenomenology [24]. [PERSON] established the generalized Bouc-Wen model to accurately describe the nonlinear phenomenon of the piezoelectric actuator, and then compensated the hysteresis effect to solve the problem [25; 26]. [PERSON] proposed a Traceless Kalman Filter to identify the parameters of the hysteretic model, and the effectiveness of this method was verified by numerical simulation and experiments [27]. [PERSON] used the asymptotic analysis method and path-tracking method to study the resonance dynamics behavior of nonlinear structures [28]. [PERSON] analyzed the modified Bouc-Wen model with MATLAB and established the nonlinear hysteretic suspension model. The frequency response characteristics of a semi-active suspension were studied [29].