Targeted energy transfer and non linear energy sinks
Résumé
It has been proved (analytically, numerically and experimentally) that by endowing nonlinear innate of some special light attachments, namely nonlinear energy sink (NES), it is possible to localize the energy and passively controlling important oscillators. The phenomenon is called energy pumping or targeted energy transfer. The process of energy pumping is mixture of nonlinear interactions between coupled oscillators which follows by bifurcation(s) and attractions to periodic regime(s) and/or strongly modulated responses (SMR). The phenomenon has applications in the field of civil and mechanical engineering (e.g. passive control of buildings and cars) and in acoustics (e.g. low frequency noise reduction by using nonlinear membranes) . For this research we have considered energy pumping problem between different types of main oscillators (linear, non smooth and Bouc Wen) and a non smooth NES. Analytical developments for one of considered systems will be presented: Invariant manifold of the system and its stability borders at fast time scale will traced. Then, the reduced order of the system at slow time scale will be analyzed in order to detect its fixed points and fold singularities which lead the system to periodic regimes and SMR, respectively. Finally, analytical predictions will be compared with numerical results. All of these developments can be endowed for designing efficient NES systems for the sake of localization and passive control of structures.