Equivalent Representation Form of Oscillators with Elastic and Damping Nonlinear Terms

Figure 4

Amplitude-time response curves of (19) and (22). The parameter values are 𝛼=1, 𝛽=1, 𝛾=0.1, 𝜐₀=0.05, 𝜂₀=0.15, 𝜅₀=0.1, 𝜔_𝑓=2.75, and 𝑄=1, with 𝑥₀=1 and 𝑥̇(0)=0. Here 𝛿=0.9975, 𝜖=1.0679, 𝜐₁=1.2806, and 𝑐=−0.0045, with 𝜎=0.645 and 𝜐=0.11. (a) Morlet continuum wavelet transform plot; (b) transient response phase portrait on 0⩽𝑡⩽50; (c) the steady-state system response phase portrait on 750⩽𝑡⩽800; (d) amplitude-time response curves. Here the solid lines represent the numerical integration solution of (19), while the red dots represent predicted values obtained by using the derived equivalent equation of motion (22).