Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator

Figure 2

Phase portraits and amplitude-time response curves for parameter values of 𝜀=0.02, 𝜎_𝑒=0.497, 𝜈=0.01, 𝐹=0.1, 𝜔_𝑓=1.1, 𝐷₁(0)=−0.541, 𝐷₂(0)=0.0653, 𝑏(0)=−0.0086, 𝑘₁(0)=0.05418, 𝜔₁(0)=1.0144, 𝐶=0.5496, and initial conditions 𝑥(0)=0 and 𝑥̇(0)=0.0663. (a) Amplitude-time transient curves on 𝑡[0,31.5]; (b) amplitude-time response curve on 𝑡[0,700]; (c) transient response phase portrait; (d) steady-state system response phase portrait on 𝑡[650,700]. The solid lines represent the numerical solution, and the dashed lines represent the proposed EBM solution.

(a)

(b)

(c)

(d)