MS13.5: Energy Transfer and Harvesting in Nonlinear Systems

The paper addresses the supratransmission (ST), i.e., emergence of the propagating waves in a nonlinear chain forced in the attenuation zone of the linear substructure. In the considered model, the nonlinearity is realized through impacts of particles in a linear chain with on-site constraints. This special form of the nonlinearity allows deriving the exact solutions for edge states of the semi-infinite boundary-driven chain. Stability of these edge states is assessed through semi-analytic procedure for direct evaluation of the monodromy matrix. The ST appears when the instability of the localized edge states leads to solutions with frequency components belonging to the propagation zone of the linear substructure. This mechanism substantially differs from previously observed ST scenarios, related to a generation of the propagating breathers. Various bifurcation sequences eventually leading to the ST are revealed and discussed.

Intermodal Targeted Energy Transfer (IMTET) is a new methodology for mitigation of undesired vibrations by facilitating the energy transfer between the modes and effective utilization of internal damping capacity of the structure. The method is based on introduction of substantially nonlinear elements that enable intensive transfer of energy between the structural modes. Previous studies on the topic primarily relied on direct optimization of the system parameters. In current presentation, a simple IMTET arrangement comprising a cantilever beam with a single impact constraint is considered. This benchmark model allows direct assessment of the modal interactions and rearrangement, depending on the initial conditions and details of the system structure. Then, one can assess the optimality of particular design solutions. Main conclusion is the relative robustness of the optimal design with respect to varying external excitations.

This work investigates the dynamic behavior of a Van der Pol oscillator (used as an archetypal self-sustained oscillator) coupled to a bistable nonlinear energy sink (BNES). First, numerical simulations show that this system can undergo a wide diversity of motions including different types of periodic regimes and so-called strongly modulated responses (SMR) as well as chaotic regimes. We also show that a BNES can be much more efficient than a classical cubic NES but a little perturbation can switch the system from harmless to harmful situations. However, even in the most unfavorable cases, a set of parameters can be found for which the BNES performs better than the NES. A fast-slow analysis of the amplitude-phase modulation dynamics (APMD) obtained by means of the so-called Multiple Scale/Harmonic Balance Method is then conducted within the framework of the geometric singular perturbation theory. A global stability analysis is partially performed from the computation of the so-called critical manifold and the APMD fixed points. This leads to interpret a certain number of regimes observed previously on numerical simulations of the initial full-order dynamics.