Attractors of harmonically forced linear oscillator with attached nonlinear energy sink I: Description of response regimes

Abstract

A series of two papers is devoted to detailed investigation of the response regimes of linear oscillator with attached nonlinear energy sink (NES) under harmonic external forcing and assessment of possible application of the NES for vibration absorption and mitigation. The first paper of the series is devoted to analytic and numeric description of the attractors (response regimes) of the system. Analytic approach is based on averaging and multiple-scales analysis, the mass ratio being used as the small parameter. The problem of possible coexistence of different attractors is reduced to analysis of flow on slow invariant manifolds (SIM) of the system. Numeric simulation confirms the predictions of the analytic model concerning the number, the shape, and the structure of the response regimes and reveals some other features of these attractors.

Responses of a two degree-of-freedom system coupled to a nonlinear damper under multi-forcing frequencies

“…For a system with one tube only, as studied before [7,8], a harmonic excitation can produce a strongly modulated response, indicating an alternation of modes corresponding successively to resonance build up and TET. For more complicated systems, the analysis is less easy but the same ideas can be considered as a basis of reflection.…”

“…Weakly quasi-periodic responses and strongly quasi-periodic responses (also named "strongly modulated responses") can exist or coexist [7,8]. The very important point is that this peak reduction can occur in a wide frequency band, with the NES adapting itself to the resonance frequencies of the primary system.…”

Vibration absorption with a nonlinear absorder including time delay

“…The complexification method combined to the averaging method will be applied starting from the equations of motion (7)(8).…”

“…Weakly quasiperiodic responses and strongly quasiperiodic responses (also named "strongly modulated response") can exists or coexist [7]. The very important point is that this peak reduction can occur in a wide frequency band, with the NES adapting itself to the resonance frequencies of the primary system.…”

The Experimental Performance of a Nonlinear Dynamic Vibration Absorber

“…Zhu et al [6] studied the system with nonlinear damping and nonlinear springs, they found that a reduction of the vibration amplitude can be obtained by adjusting the parameters of the nonlinear dampers, nonlinear spring stiffness and excitation frequency. It has also been demonstrated [7][8][9][10] that the primary phenomena behind the energy pumping produced is due to resonant interactions between coupled linear and nonlinear components.…”