Abstract:

Acoustic black hole effect (ABH) refers to a passive vibration mitigation technique which takes advantage of flexural wave properties in thin structures with variable thickness. Focusing on the problem that the classical linear ABH is efficient only at high frequency range but less than desirable in the low frequency domain, this paper proposes the idea of using contact nonlinearity to transfer the energy from low to high frequency range, in order to improve the overall efficacy of the ABH. Considering the vibration of an ABH beam in contact with a rigid barrier from below it, an experimental study is firstly carried out to show the nonlinear phenomena and energy transfer induced by the contact nonlinearity. Then, a numerical model is derived from Euler-Bernoulli beam theory, with convergence properties studied. The model follows the general procedures of modal approach, while the eigenvalue problems are computed using a finite difference method due to thickness variation. The contact force is handled by Hertzian contact law, and the damping layer is dealt with a Ross-Kerwin-Ungard model. Detailed studies considering contact nonlinearity are thus conducted to precisely quantify the energy transfer and decay, and the gain in efficiency of the ABH, with parametric effect respect to the contact stiffness, initial gap and longitudinal location of contact points. It is demonstrated that when the contact nonlinearity is induced to the system, the vibrational energy can be transferred from the low frequency band-where the ABH is inefficient, to the high frequency range-where the ABH is effective, the energy decay in the beam is remarkably accelerated, and the overall performance of the ABH effect is significantly improved.

Key words: acoustic black hole, damping, vibration suppression, energy transfer, contact nonlinearity