Quasi-periodic oscillation characteristics of a nonlinear energy sink system under harmonic excitation

Abstract

Quasi-periodic oscillation characteristics of a nonlinear energy sink (NES) system under harmonic excitation are studied in this work. It is found that there exist uniformly distributed sidebands in frequency spectra of quasi-periodic oscillations. The traditional incremental harmonic balance (IHB) method and the IHB method with two time-scales are used to obtain accurate frequency components and amplitudes of periodic responses and two different quasi-periodic oscillations of the system, respectively, with variations of the external excitation frequency and amplitude. The two different quasi-periodic oscillation characteristics are analyzed; energy absorption of the NES system under different excitation frequencies and amplitudes is also analyzed. Stability of quasi-periodic solutions obtained from the IHB method with two time-scales is analyzed by the Floquet theory. Analytical results obtained from the traditional IHB method and the IHB method with two time-scales agree very well with those from numerical integration using the fourth-order Runge–Kutta method. Results show that the efficiency of energy absorption of a strongly quasi-periodic oscillation is greater than those of a periodic response and a weakly quasi-periodic oscillation.