Romanian Journal of Acoustics and Vibration, cilt.22, sa.1, ss.32-38, 2025 (ESCI, Scopus)
The effect of external excitation frequency variation on the vibrations of a damped cubic nonlinear equation is investigated. Three types of frequency variations are considered: Decaying type variation, built-in type variation, and harmonic variation. Approximate solutions are constructed using the Method of Multiple Scales. Steady-state deterministic solutions are possible in the first two cases for long time scales. In the harmonic variation case, steady-state solutions are not possible, and the amplitudes and phases do not tend to a constant value. Direct integration of the model depicts the chaotic behavior of the system.