A Transformation Method for Solving Conservative Nonlinear Two-Degree-of-Freedom Systems

Figure 3

Amplitude-time response curves computed from the numerical integration solutions of (21) and those provided by substituting (23)₁ into (21)₂. The parameter values used to obtain these plots were 𝛽=1/5 and 𝑟₂=1, 𝜀=50, with 𝜎₁₀(0)=1, 𝜎̇(0)=0, 𝑧₁₀(0)=−1, 𝑧(̇0)=0, and 𝑢₁=−0.4, 𝑢₂=0.1, 𝑢₃=−0.01, and 𝑢₄=−0.315. Here, the gray solid lines describe the numerical integration solutions of (21), while the blue dashed lines represent the numerical solutions obtained from the derived equivalent nonlinear equations of motion. In this case, the computed RMSE values were 0.1006, for 𝑦₁, and 0.0102, for 𝑦₂.

(a)

(b)