# Vibration Response Law of Aircraft Taxing under Random Roughness Excitation
## 5 Results and Discussion
### Vibration Response Analysis of Aircraft Taxing under Stochastic Structural Parameters  
Due to the large number of degrees of freedom in the aircraft model, it is complicated to theoretically derive the effect of stochastic structural parameters on the vibration response. The Monte Carlo method can build a mathematical model of the input and output variables, apply the probability distribution of each variable to random sampling, and calculate the output variables using the randomly generated input variables. By repeating the random simulations, the probability distribution function of a certain output variable can be obtained. Additionally, the accuracy of the output variable's probability distribution function increases with the number of simulations. With the aid of the MATLAB (R2019a) software and the Monte Carlo method, this paper analyzes the variation in each vibration response when the probability density function of aircraft structural parameters is modeled as a normal distribution.  
The variation coefficients of the sprung mass, rotational inertia, stiffness coefficient of the landing gear buffer, damping coefficient of the landing gear buffer, stiffness coefficient of the tire, and damping coefficient of the tire are all set to 0.05. By using the Monte Carlo method to randomly sample 1000 times at a time, the variation coefficient distribution of the variance of CGA, PSA, NGDLC, and MGDLC can be obtained, as shown in Figure 9.  
Figure 7: PSD distribution of vibration response during takeoff: (**a**) PSD distribution of CGA; (**b**) PSD distribution of PSA; (**c**) PSD distribution of MGDLC; (**d**) PSD distribution of NGDLC.  
The influence of the sprung mass is the largest, having a significant effect on the four vibration responses, with variation coefficient values exceeding 0.05. Among them, the sprung mass has the greatest impact on NGDLC, reaching 0.113. The rotational inertia mainly affects PSA, with variation coefficients above 0.05, but has little effect on the other  
Figure 8: PSD distribution of vibration response during landing: (**a**) PSD distribution of CGA; (**b**) PSD distribution of PSA; (**c**) PSD distribution of MGDLC; (**d**) PSD distribution of NGDLC.  
Figure 9: Variation coefficient of vibration response variance under random structural parameters.  
three vibration responses. The damping coefficient of the landing gear buffer has a greater impact than the stiffness coefficient of the landing gear buffer. The damping coefficient of the front landing gear affects PSA and NGDLC more, while the damping coefficient of the main landing gear has a greater impact on CGA and MGDLC, as the center of gravity is closer to the main landing gear. The situation with the tire is the opposite of that of the landing gear, with the tire damping coefficient having a much smaller effect than the tire stiffness. The stiffness coefficient of the tire has a great influence on the dynamic load coefficient of the landing gear where it is located, but it has little effect on the other landing gear. At the same time, the stiffness coefficient of the main landing gear tire has a greater impact on the fuselage vibration than the front landing gear, indicating that more attention should be paid to the roughness excitation applied to the main landing gear.