..., sinusoidal excitation. In the theoretical analysis, van der Pol's method is employed to determine the expressions for the frequency response curves for fundamental harmonic oscillations. In the numerical calculations, the frequency response curves are presented for N = 2 and 3 and compared with the results...

... as (4) x i = u i cos ω t - ν i sin ω t = A i cos ( ω t + φ i )     ( i = 1 , 2 , … , N ) Figure 12 shows the frequency response curves when the value of K 1 is increased from 0.005 in Fig. 11 to 0.01. Saddle-node...

... the frequency response curves for a rectangular tank system with a high liquid level, which can be numerically calculated from Eq. (24) . The values of the dimensionless parameters are ν 0  = 0.93, ν 1 (=1 −  v 0 ) = 0.07, k  = 4.0, c  = 0.02, h  = 0.6, w  = 2.0, ζ ij  = 0.015, and F 0  = 0.0013...

... of motion for the structure and the modal equations of motion for the first, second, and third sloshing modes are derived by using Galerkin’s method, taking into account the nonlinearity of the sloshing. Then, van der Pol’s method is employed to determine the frequency response curves. It is found...

...Takashi Ikeda The nonlinear responses of a single-degree-of-freedom system with two pendulum tuned mass dampers under horizontal sinusoidal excitation are investigated. In the theoretical analysis, van der Pol’s method is applied to determine the expressions for the frequency response curves...

...Takashi Ikeda The characteristics of two, three, and four nonlinear vibration absorbers or nonlinear tuned mass dampers (NTMDs) attached to a structure under harmonic excitation are investigated. The frequency response curves are theoretically determined using van der Pol’s method. When...