On the dynamics around targeted energy transfer for vibro-impact nonlinear energy sink

Abstract

A periodically forced linear oscillator with impact attachment has been studied. An asymptotical analytical method has been developed to obtain the fixed points and to analyze the transient 1:1 resonance (two impacts per cycle) of the modulated response. The influence of parameters on dynamics has been analyzed around the Slow Invariant Manifold (SIM). Five different response regimes have been observed from theoretical and numerical results. It is demonstrated that they are closely related to the topological structure and relative position of fixed points. The bifurcation, route to chaos and the efficiency of Targeted Energy Transfer (TET) with the variation of different parameters (i.e. amplitude and frequency of excitation, clearance, damping, mass ratio and restitution coefficient) have been investigated and well explained around SIM. Experimental results validate the existence of different regimes and different routes to chaos by the variation of the return map of time difference between consecutive impact moments. TET phenomenon has been analyzed for a strongly modulated response and different cases of TET have been observed and analyzed. It is clearly observed that TET depends not only

Optimization mechanism of targeted energy transfer with vibro-impact energy sink under periodic and transient excitation

“…A design procedure [24] is proposed and the suggested optimum regime is actually corresponding to the minimal point in the slow invariant manifold (SIM) [19]. There are some discrepancy between analytical calculations and numerical results because that the proposed analytical solution may not be stable [25]. The edge of chaos, i.e.…”

“…Based on the already developed asymptotic method [18][19][20], a general equation governing the variation of motion, e.g., the resonance part of SMR, is developed for both cubic and VI NES [28], in which the interaction force between NES and main structure plays the central role in explaining the variation of different response regimes. As a further study of VI NES, the study of the influence of parameters on dynamics is improved [25] from the previous study of different parameters in a separate way to the study of different parameters as a whole. By this way, their mutual influence and the same underlying mechanism is clearer.…”

“…zero amplitude of outside force), only the latter is analyzed. The objective here is to apply the asymptotic method used in a series of papers [18][19][20]25,28] to obtain the possible optimization design criterion of the system with damping rather than its underlying Hamiltonian system.…”

Seismic performance of a nonlinear energy sink with negative stiffness and sliding friction

“…We utilized such sliding friction as damping of the present NES, as it is simpler to implement than viscous damping. Moreover, we neglected frictions of the two guiders coupled to the springs, as they are nonbearing components with much smaller friction forces. Hence, the reaction force of the present NES is where k and l are the constant stiffness and relaxation length of the hinged spring, respectively, and …”

“…McFarland et al realized the cubic NES (Type I NES) by using transverse elastic wire that yields geometrically nonlinear restoring force. Nucera et al, Ahmadi et al, Gendelman et al, and Li et al presented vibro‐impact NESs, which can absorb the vibration energy of the primary structure by transient internal resonance captured at high frequencies. Luo et al completed the shake table test on the large‐scale structure model, for which cubic NES and vibro‐impact NES were adopted for seismic control.…”