Equivalent Mathematical Representation of Second-Order Damped, Driven Nonlinear Oscillators

Figure 1

Amplitude-time response curves obtained from the numerical integration solution of (12) and (13) for the system parameter values of 𝜈=0.01, 𝐴=3, 𝐵=−4, 𝐺=1, 𝑄₀=0.1, and 𝜔_𝑓=3 with 𝑦(0)=1/2 and 𝑦(̇0)=0. Here, the black solid line represents the numerical integration solution of (12), while the red dashed line represents the prediction obtained by using the derived equivalent equation of motion (13) with 𝛿=2.8713, 𝜖=−0.7178, 𝜈₁=0.0101, 𝜎=2.1191, and 𝜐=−350.4.