# Analysis of Dynamic Characteristics of Attached High Rise Risers
## 3 Dynamic Analysis of VNA System under Combined Excitation
### System Vibration Response Analysis under Design and Accident Conditions  
When designing the VNA system of Hualong-1, the load combinations are divided into the following two types of working conditions for calculation [46; 47]:  
1. Design condition (level O, level A): dead weight + accessory load + OBE seismic load + 100 year return period strong wind load. 2. Accident condition (level D): (1) dead weight + accessory load + 71.4 m/s tornado load; (2) dead weight +accessory load + SSE seismic load. In order to simplify calculations and provide design optimization ideas, this chapter simplifies and adjusts the working conditions. The design working condition combination remains unchanged. The once-in-a-century wind speed load is \(V_{out}=68\) m/s, and the OBE seismic load is from the nuclear power ACP1000 reactor type using a standardized design. On the basis of eight foundation section parameters, the ground action peak value is 0.1 g, and the frequency is widened by 15%. The seismic response spectrum obtained from the calculation result envelope value is taken. Here, the basic acceleration excitation is simplified for convenience of calculation, \(\ddot{\eta}_{b}(\tau)=\sum\limits_{i=1}^{5}m_{i}f_{ai}\cos(\Omega_{gi}\tau)\). The basic excitation contains five frequency components, corresponding to the first to fourth order resonant frequencies and non-resonant frequency components of the system, \(\Omega_{g1}=0.5L^{2}\sqrt{m_{\Sigma}/(EI)}\), \(\Omega_{g2}=1.128L^{2}\sqrt{m_{\Sigma}/(EI)}\), \(\Omega_{g3}=7.174L^{2}\sqrt{m_{\Sigma}/(EI)}\), \(\Omega_{g4}=20.328L^{2}\sqrt{m_{\Sigma}/(EI)}\), \(\Omega_{g5}=40.177L^{2}\sqrt{m_{\Sigma}/(EI)}\). \(f_{ai}\) is the acceleration excitation amplitude corresponding to each frequency component, \(f_{a1}=0.9\) g, \(f_{a2}=1.8\) g, \(f_{a3}=1.4\) g, \(f_{a4}=0.9\) g, \(f_{a5}=0.5\) g. \(m_{i}\) is the mass fraction of each frequency component of the base acceleration excitation, \(m_{1}\)= 5%, \(m_{2}\)= 70%, \(m_{3}\)= 10%, \(m_{4}\)= 10%, \(m_{5}\)= 5%, and the sum of them is 1. Due to the high wind speed in the external flow field, it is not within the frequency locking region of the system's vortex induced vibration. Based on modal truncation analysis, it is easy to know that when considering the combined effects of vortex induced vibration and foundation excitation, the fourth order modal truncation should be selected for analyzing the vibration response of the VNA system structure. In this section, the Runge-Kutta method is used for numerical calculation of Equations (26) and (27), and the initial value of the calculation is 0. The physical parameters are shown in Table 1. The linear and nonlinear stiffness values of the elastic constraint are taken as \(10^{3}\) N/m and \(10^{3}\) N/m\({}^{3}\). The dimensionless flow velocity in the pipe is taken as 0.5, regardless of structural damping, and the elastic constraint damping coefficient is 0.3 N/(m/s). The time history response curve and phase diagram of the free end of the VNA system structure can be obtained through calculation, as shown in Figure 9.  
Figure 9a shows that the system exhibits a phenomenon similar to multistable vibration under the conditions of multi-frequency foundation excitation and high-velocity vortex-induced vibration. However, the motion changes around the time history response wave peaks and valleys are relatively severe, which can also be seen from the phase diagram of Figure 9b. The phase trace at the free end of the VNA system exhibits a quasi-multistable periodic motion. This is because, under the action of high wind speed in the external flow field, high-frequency vortex shedding causes VIV to superimpose on the basic excitation vibration, causing the system to experience slight shaking while undergoing periodic motion.