Recently, it has been demonstrated that a vibro-impact type nonlinear energy sink (VI-NES) can be used efficiently to mitigate vibration of a linear oscillator (LO) under transient loading. The objective of this paper is to investigate theoretically and experimentally the potential of a VI-NES to mitigate vibrations of an LO subjected to a harmonic excitation (nevertheless, the presentation of an optimal VI-NES is beyond the scope of this paper). Due to the small mass ratio between the LO and the flying mass of the NES, the obtained equations of motion are analyzed using the method of multiple scales in the case of 1:1 resonance. It is shown that in addition to periodic response, system with VI-NES can exhibit strongly modulated response (SMR). Experimentally, the whole system is embedded on an electrodynamic shaker. The VI-NES is realized with a ball which is free to move in a cavity with a predesigned gap. The mass of the ball is less than 1% of the mass of the LO. The experiment confirms the existence of periodic and SMR regimes. A good agreement between theoretical and experimental results is observed.

In this paper we describe the modeling of the hysteretic behavior of belt tensioners. An initial experimental device is composed only of the tensioner by using forcing frequencies, preloads and deflection amplitudes. It permits the identification of the parameters of the restoring force model used. Comparison of the measured and predicted force-deflection loops of the tensioner subjected to large deflections permits preliminary validation of the model. The second experimental device consists of a belt-tensioner system. Its non-linear modeling includes the above hysteretic model and the belt’s longitudinal characteristics. Validation of the belt-tensioner model is completed by comparing the measured and predicted belt tension. Finally, it is shown by using a parametric investigation and phase-plane portrait that the response of the belt-tensioner system increases with the frequency and the amplitude of the excitation.

In this paper, the dynamic response of a harmonically forced linear oscillator (LO) strongly coupled to a nonlinear energy sink (NES) is investigated both theoretically and experimentally. The system studied comprises an LO with an embedded, purely cubic NES. The behavior of the system is analyzed in the vicinity of 1:1 resonance. The complexification-averaging technique is used to obtain modulation equations and the associated fixed points. These modulation equations are analyzed using asymptotic expansion to study the regimes related to relaxation oscillation of the slow flow, called strongly modulated response (SMR). The zones where SMR occurs are computed using a mapping procedure. The slow invariant manifolds (SIM) are used to derive a proper optimization procedure. It is shown that there is an optimal zone in the forcing amplitude-nonlinear stiffness parameter plane, where SMR occurs without having a high amplitude detached resonance tongue. Two experimental setups are presented. One is not optimized and has a relatively high mass ratio (≈13%) and the other one is optimized and exhibits strong mass asymmetry (mass ratio ≈1%). Different frequency response curves and associated zones of SMR are obtained for various forcing amplitudes. The reported experimental results confirm the design procedure and the possible application of NES for vibration mitigation under periodic forcing.