Limiting phase trajectories and nonstationary resonance oscillations of the Duffing oscillator. Part 2. A dissipative oscillator

作者：Manevitch L I^*; Kovaleva A S; Manevitch E L; Shepelev D S

来源：Communications in Nonlinear Science & Numerical Simulation, 2011, 16(2): 1098-1105.

DOI：10.1016/j.cnsns.2010.04.033

• Resonance oscillations
• Phase transitions
• Asymptotic methods
• Limiting phase trajectories

This paper extends the concept of limiting phase trajectories (LPT) to systems with dissipation. The Duffing oscillator with linear dissipation and periodic excitation is studied. Under condition of 1:1 resonance, we obtain an approximate analytic solution describing two stages of motion: at the first stage the trajectory is close to the non-dissipative LPT, while at the second stage the trajectory approaches stationary oscillations near the steady state.

• 出版日期2011-2