Acoustic ‘black holes’ for flexural waves as effective vibration dampers

Elastic plates of variable thickness gradually decreasing to zero (elastic wedges) can support a variety of unusual effects for flexural waves propagating towards sharp edges of such structures and reflecting back. Especially interesting phenomena may take place in the case of plate edges having cross-sections described by a power law relationship between the local thickness h and the distance from the edge x: h(x)=εxm, where m is a positive rational number and ε is a constant. In particular, for m⩾2—in free wedges, and for m⩾5/3—in immersed wedges, the incident flexural waves become trapped near the edge and do not reflect back, i.e., the above structures represent acoustic ‘black holes’ for flexural waves. However, because of the ever-present edge truncations in real manufactured wedges, the corresponding reflection coefficients are always far from zero. The present paper shows that the deposition of absorbing thin layers on the plate surfaces can dramatically reduce the reflection coefficients. Thus, the combined effect of the specific wedge geometry and of thin absorbing layers can result in very efficient damping systems for flexural vibrations.