Energy transfer for enhanced acoustic black hole effect through a cable-induced mechanical nonlinearity

Acoustic black hole (ABH) structures hold great promise for numerous engineering applications. Stemming from a power-lawed thickness decrease, bending waves are slowed down to produce wave compression and energy concentration, conducive to vibration/sound radiation control and energy harvesting. However, in existing linear studies, the ABH effect shows a deficiency at low frequencies, typically below the so-called cut-on frequency. In this paper, mechanical nonlinearity is introduced into a cantilever ABH beam to enhance the low-frequency ABH effect through low-to-high frequency energy transfer. Using a grounded cable with cubic stiffness, the sweeping results (with excitation frequency below the cut-on frequency) show that the displacement of the low-order modes of the nonlinear ABH beam decreases while the amplitude of its high-order harmonics increases compared to that of its linear counterpart, indicating a significant energy transfer phenomenon enabled by the cable in the nonlinear system. Due to the inherent ABH effect at high frequencies, the damped nonlinear ABH beam absorbs the transferred energy to result in a reduction of the vibration amplitude. To quantify the ABH effect under nonlinear conditions, the damping loss factor of the system is evaluated from energy viewpoint alongside the harmonic balance method. Below the cut-on frequency, the damping loss factor of some dominant modes in the ABH beam is drastically increased, indicating an enhanced ABH effect. This is also confirmed by the time response in the free decay test. Experiments demonstrate the energy transfer phenomenon and the efficient damping effect achieved in the nonlinear system.