Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator

Figure 1

Evolutive amplitude-frequency response curves of a rigid body supported symmetrically by a simple shear spring and sliding over a smooth inclined bearing surface with moderate static shear deflection 𝜎_𝑒=0.497 and parameter values of 𝜀=0.02, 𝐹=0.1, 𝜈=0.01, and initial conditions 𝑥₀=1 and 𝑥̇₀=−0.0091. At 𝑡=0, the initial values of 𝑏, 𝐶, 𝐷₁, 𝐷₂, 𝑘₁, and 𝜔₁ are given as 𝑏(0)=−0.0121, 𝐶=0.9951, 𝐷₁(0)=0.0962, 𝐷₂(0)=0, 𝑘₁(0)=0.0902, and 𝜔₁(0)=1.0154. The blue dot curves represent unstable system response.