Dynamics of two vibro-impact nonlinear energy sinks in parallel under periodic and transient excitations. (April 2017) - Li, T.; Gourc, E.; Seguy, S.; Berlioz, A.
Abstract: A linear oscillator (LO) coupled with two vibro-impact (VI) nonlinear energy sinks (NES) in parallel is studied under periodic and transient excitations, respectively. The objective is to study response regimes and to compare their efficiency of vibration control. Through the analytical study with multiple scales method, two slow invariant manifolds (SIM) are obtained for two VI NES, and different SIM that result from different clearances analytically supports the principle of separate activation. In addition, fixed points are calculated and their positions are applied to judge response regimes. Transient responses and modulated responses can be further explained. By this way, all analysis is around the most efficient response regime. Then, numerical results demonstrate two typical responses and validate the effectiveness of analytical prediction. Finally, basic response regimes are experimentally observed and analyzed, and they can well explain the complicated variation of responses and their corresponding efficiency, not only for periodic excitations with a fixed frequency or a range of frequency, but also for transient excitation. Generally, vibration control is more effective when VI NES is activated with two impacts per cycle, whatever the types of excitation and the combinations of clearances. This observation is also well reflected by the separate activation of two VI NES with two different clearances, but at different levels of displacement amplitude of LO. Abstract : Highlights: This paper analytically treats a strongly nonlinear system with two vibro-impact (VI) nonlinear energy sinks (NES) and tries to find the solutions of response regimes with sustained or transient two impacts per cycle. Different basic response regimes are experimentally observed and are applied to explain complicated nonlinear dynamics resulting from VI. Nonlinear targeted energy transfer is experimentally found relatively optimal for the response regime with two impacts per cycle, no matter under periodic or transient excitations. The optimization design of two VI NES in parallel is to make as much VI NES activated with the response regime of two impacts per cycle as possible. This principle is experimentally validated by the separate activation of two VI NES with different clearances.