Wave propagation in locally resonant cylindrically curved metamaterial panels

Combining lightweight characteristics with favourable noise and vibration behaviour, locally resonant metamaterials with vibro-acoustic stopband behaviour are gaining increasingly more attention. In view of applicability of metamaterials, this paper investigates the effects of curvature on stopband behaviour. Through derivation of curved unit cell models, dispersion curves for cylindrically curved infinite periodic structures are derived. The effect of curvature on metamaterials is investigated through both an academic example of an infinite cylindrically curved panel with added spring-mass systems and a realizable curved panel with resonant structures. It is shown that, whenever pure flexural motion exists in the host structure, the stopband mechanism can be applied to achieve flexural stopbands.