Equivalent Representation Form of Oscillators with Elastic and Damping Nonlinear Terms

Figure 5

Amplitude-time response curves of (25) and (29). The parameter values are 𝑚=3/2, 𝐴=1, 𝜔_𝑛=1, ℎ=1, 𝑄₀=1, 𝜈=0.1, 𝜅=0.9, and 𝜔_𝑓=0.75, with 𝑥₀=1 and 𝑥̇(0)=0. (a) Amplitude-time response curves for 𝑝=1/4; (b) amplitude-time response curves for 𝑝=3/4; (c) amplitude time-response curves for 𝑝=1.5; (d) amplitude-time response curves for 𝑝=2.75. Here the solid black lines represent the numerical integration solution of (25), while the red dots represent the prediction obtained by using the derived equivalent equation of motion (29).

(a)

(b)

(c)

(d)