2020/03/13 by Agnessa Kovaleva, Kovaleva, Agnessa
Computer Science · Engineering · Physics and Astronomy · #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS) #Vibration and Dynamic Analysis
paper · pdf · doi:10.48550/arxiv.2003.06346
openalex publication_date 2020/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we develop an analytical framework to explain the influence of dissipation and detuning parameters on the emergence and stability of autoresonance in a strongly nonlinear weakly damped chain subjected to harmonic forcing with a slowly-varying frequency. Using the asymptotic procedures, we construct the evolutionary equations, which describe the behavior of the array under the condition of 1:1 resonance and then approximately compute the slow amplitudes and phases as well as the duration of autoresonance. It is shown that, in contrast to autoresonance in a non-dissipative chain with unbounded growth of energy, the energy in a weakly damped array being initially at rest is growing only in a bounded time interval up to an instant of simultaneous escape from resonance of all autoresonant oscillators. Analytical conditions of the emergence and stability of autoresonance are confirmed by numerical simulations.