Flexural wave induced coherent scattering in arrays of cylindrical shells in water

Abstract

A periodic array of elastics shells in water is a sonic crystal with local resonances in the form of flexural vibrations. This acoustic metamaterial has seen application in wave steering by grading the index in the array, as well as acoustic filters manifested by Bragg scattering. The primary reason for using shells is that they can be tuned quasi-statically to have water-like effective acoustic properties. The issue is that the modally dense flexural resonances can form pseudogaps in the frequency response resulting in total reflection from the array. Furthermore, if a flexural resonance falls in the Bragg band gap, total transmission is possible at that frequency. Although the scattered wave due to low order flexural vibration of a thin shell is evanescent, when several shells are closely spaced, the effect on the far-field response is dramatic. In this paper, the interaction of neighboring shells is investigated theoretically using the Love-Timoshenko shell theory and multiple scattering. A simple model is offered to describe the interaction of modes based on the analytical work. The directionality of the lowest flexural modes is also discussed as it can lead to phasing between neighboring shells.