## 3 Results and Discussion
### Influence of Bending-Torsional Coupled Effect on Nonlinear Aerodynamics
In order to explore the law that the proportion of nonlinear aerodynamic components change with the coupled amplitude, the sum of the second to fifth harmonic components is used to represent the aerodynamic nonlinear components, and the total amount of the previous quintuple frequency is used as the cardinal number of normalized statistics, as shown in Figures 18-21. Compared with the 1-DOF pitching motion, the proportion of nonlinear components of aerodynamic force is reduced due to the addition of a small amplitude having motion, as shown in Figures 18a and 19a. At this time, the heaving motion plays a positive damping role, and the positive damping action of the heaving motion decreases obviously with the increase in foundational pitching amplitude. For the aerodynamic lift, as shown in Figure 18b, the proportion of nonlinear components decreases first and then increases with heaving amplitude, and the heaving motion has an extreme value amplitude of positive damping action. For the aerodynamic moment, as shown in Figure 19b, the proportion of nonlinear components generally shows a positive correlation trend with increasing the heaving amplitude. In the 1-DOF pitching motion  
Figure 16: Variation in Fourier amplitude of aerodynamic lift with pitching amplitude. (**a**) The fundamental frequency; (**b**) Second harmonic and third harmonic. Figure 17: Variation in Fourier amplitude of aerodynamic moment with pitching amplitude. (**a**) The fundamental frequency; (**b**) Second harmonic and third harmonic. nonlinear components of aerodynamic lift is higher than that of aerodynamic moment, which has stronger nonlinear characteristics. However, due to the positive damping effect of small amplitude heaving motion, a slightly higher proportion of aerodynamic moment is observed near the extreme value amplitude of positive damping action. Therefore, the complex influence of a heaving motion amplitude on nonlinear characteristics should be considered when studying nonlinear flutter. Figures 20a and 21a show that compared with the 1-DOF heaving motion, the nonlinear components of aerodynamic moment increase with the addition of pitching motion, and the same results are also observed in the aerodynamic lift under the foundational heaving motion of small amplitude. The nonlinear aerodynamic components broadly positively correlated with the pitching amplitude, as reported in Figures 20b and 21b. Under different foundational heaving amplitudes, the difference in proportion of nonlinear components of aerodynamic forces (especially aerodynamic moment) decreases obviously with the increase in pitching amplitude. In conclusion, it is considered that the nonlinear components of aerodynamic forces in the coupled motion are mainly provided by pitching motion form, and the aerodynamic moment is more significantly affected by the pitching motion. In general, the proportion of nonlinear components of aerodynamic lift is higher than  
Figure 19: Proportion variation in high-order harmonic components of aerodynamic moment with different heaving amplitudes. (**a**) Comparison of 1-DOF pitching motion with 2-DOF coupled motion; (**b**) 2-DOF coupled motion. Figure 18: Proportion variation in high-order harmonic components of aerodynamic lift with different heaving amplitudes. (**a**) Comparison of 1-DOF pitching motion with 2-DOF coupled motion; (**b**) 2-DOF coupled motion. that of aerodynamic moment, which has stronger nonlinear characteristics. Therefore, the nonlinear components of aerodynamic lift should be considered preferentially when optimizing the nonlinear model. In order to compare the variation characteristics of aerodynamic lift and moment with the coupling amplitude in detail, the proportion of nonlinear components in the 1-DOF motion of the section is taken as the cardinal number for normalized statistics, as shown in Figures 22 and 23. Figure 22 shows that the positive damping action of small amplitude heaving motion in the aerodynamic lift is significantly stronger than that of aerodynamic moment.