Figures 8(a) and 8(b) show the frequency response curves of the translations *x*_{0} and *z*_{0} for the 2DOF system, respectively; Figs. 8(c)–8(e) for blade inclinations *θ*_{i} (*i* = 1, 2, 3), respectively. These curves are obtained by applying the swept-sine test to Eq. (9), which includes the nonlinear terms in real wind turbines. The values of the wind turbine's parameters are *μ*_{Α} = 3.2 × 10^{−8}, *μ*_{T} = 0.94, *μ*_{ι} = 0.02, *k*_{x} = *k*_{z} = 1.0, *k*_{i} = 0.5, *l*_{i} = 40.0, *c*_{x} = *c*_{z} = 0.03, *c*_{i} = 0.04, *b*_{i} = 2.0, *α*_{1} = 0 deg, *α*_{2} = 120 deg, *α*_{3} = 240 deg, *V*_{0} = 6.0, *V*_{i} = 0.6, and *λ* = ±3.0 × 10^{−8}. The values of *l*_{i} and *k*_{i} are same as those in Figs. 6 and 7, respectively. Here, *λ* represents the acceleration of the sine sweep excitation, and *ωt* in Eq. (9) is replaced by (1/2)*λt*^{2}+*ω*_{0}*t* in the numerical calculations, where *ω*_{0} represents the initial rotational speed for the swept-sine test. The maximum amplitudes of the time histories are calculated, and these values are plotted at each rotational speed in Fig. 8, when the rotational speed is either increased or decreased. The solid (black) line represents the results when the rotational speed is increased from 0.05 to 0.20 (*λ*= 3.0 × 10^{−8}, *ω*_{0} = 0.05), and the dashed (red) line represents the results when the rotational speed is decreased from 0.20 to 0.05 (*λ*= –3.0 × 10^{−8}, *ω*_{0} = 0.20). Resonant peaks appear due to wind and parametric excitation near the rotational speeds indicated by A, B, and C, which correspond to the points of the same names in Figs. 5–7, where unstable vibrations appear in the linearized system. Note that the response curves for the three blades are identical. When the rotational speed is decreased from *ω* = 0.2, the blades vibrate at increasing higher amplitudes from point A_{2} and peak at point A_{3}, which exists out of the frame in Figs. 8(c)–8(e). Jump phenomena occur, and the amplitudes of the blades jump from point A_{3} to point A_{1}. The blades then vibrate at extremely low amplitudes until point B_{2}. The amplitudes of the blades increase again and peak at point B_{3}, also out of the frame in Figs. 8(c)–8(e). Jump phenomena occur, and the amplitudes of the blades are almost zero at point B_{1}. When the rotational speed is increased from *ω* = 0.1, the amplitudes of the blades peak at comparatively high amplitudes at point $B3\u2032$ near rotational speed B, and at lower amplitudes at point $A3\u2032$ near rotational speed A. The frequency response curves for the blades near rotational speeds A and B bend to the left, exhibiting softening behavior, because each blade is supported by a rotational spring, and thus behaves like a pendulum. In real wind turbines, starting and stopping them and/or a change in wind velocity affect the rotational speed of the blades. As demonstrated by Fig. 8, a decrease in the rotational speed may cause the blades to vibrate at higher amplitudes.