New method of damping structural vibrations based on the acoustic black hole effect

本课题的目的是根据弯曲波在幂律分布的弹性楔形结构中传播和反射的特点，开展有效的结构减振新方法的理论和实验研究。这种结构的工作原理是基于最近发现的可能发生在具有由楔形局部厚度d和到其边缘的距离x之间的幂定律关系描述的横截面的弹性楔形中的新类别的“波捕获”现象。具体地说，对于自由楔形中的幂m=2和更高，以及对于浸没的楔形中的幂m=5/3和更高，入射的弯曲波可以在边缘附近被捕获，因此它们永远不会反射回来，即上述结构实现了弯曲波的声学‘黑洞’。这种楔形结构与附着在边缘的窄条薄吸收层相结合，即使是在非理想的幂函数曲线的真实楔形的情况下，也可以提供非常低的反射，从而实现了非常有效的抑制共振弯曲振动的方法。在拟议的项目中，旨在进一步发展和研究提出的基于声黑洞效应的结构减振新方法。计划从理论和实验两方面详细研究几种有希望的具有声黑洞结构的结构。拟议项目的重点将放在所谓的二维黑洞上，这些黑洞迄今还没有被研究过。该项目的成果将导致开发新的非传统和非常有效的减震结构振动的方法，这些方法可能会在不同的工程应用中使用。

The aim of the proposed project is to carry out theoretical and experimental investigations of the new efficient method of damping structural vibrations based on the specific features of flexural wave propagation and reflection in elastic wedge-like structures of power-law profile. The principle of operation of such structures is based on the recently discovered new class of 'wave trapping' phenomena that may take place in elastic wedges having cross sections described by a power law relationship between the wedge local thickness d and the distance from its edge x. In particular, for powers m = 2 and higher - in free wedges, and for powers m = 5/3 and higher - in immersed wedges, the incident flexural waves can be captured near the edges and therefore they never reflect back, i.e. the above structures materialise acoustic 'black holes' for flexural waves. In combination with narrow strips of thin absorbing layers attached to the edges, such wedge-like structures can provide very low reflections even in the case of real wedges of non-ideal power-law profile, thus implementing very efficient way of damping resonant flexural vibrations. In the proposed project, it is intended to further develop and investigate the proposed new method of damping structural vibrations based on the acoustic black hole effect. It is planned that several promising configurations of structures with acoustic black holes will be investigated in detail both theoretically and experimentally. The emphasis in the proposed project will be made on the so-called two-dimensional black holes that have not been investigated so far. The results of the project will lead to the development of new non-traditional and very efficient ways of damping structural vibrations that eventially could be used in different engineering applications.