Wave propagation in locally resonant cylindrically curved metamaterial panels

Abstract

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.

Vibration Attenuation in Pipes: Design and Experimental Validation of a Resonant Metamaterial Solution

“…Considering the low mass of the structure, its hollowness and the fact that it is quite thin, the radiated noise from the wall of such a pipe can be considerable [18] . Moreover, as shown in [17], the circular curvature of the structure is a good demonstration of the effect of curvature on the metamaterial solution and stopband zones.…”

“…(2), the first eigenfrequency of the resonator is a flexural mode with respect to the host structure and it occurs at 745.8 Hz, while the second eigenfrequency occurs at 1059.1 Hz and can be described as a longitudinal mode with respect to the host structure. Following previous studies [9,17], it will be investigated both numerically and experimentally whether the addition of this type of resonator to a pipe can induce a stopband. …”

“…These dispersion curves provide the relationship between the wavenumbers and the frequency of the waves which can propagate in the structure. The application of Bloch-Floquet theorem for the dispersion analysis of both open cylindrical metamaterial shells and metamaterial pipes are performed by Nateghi et al [16,17]. Considering the configuration used in the current study, readers are referred to [17] for the required formulations of unit cell modelling in infinitely long cylindrical pipes.…”

“…Therefore, next to studies on the stopband behavior in flat metamaterial plates, it is worth to investigate the effect of curvature on the behavior of locally resonant metamaterials. Recently, Nateghi et al [16,17] extended the metamaterial demonstration of Claeys et al [9] to the case of infinite cylindrical shells and pipes. The results show a considerable difference in behavior due to the addition of the cylindrical curvature and the existence of cut-on frequencies.…”

“…Following form the findings of [17], a metamaterial solution for vibration attenuation of a lightweight Aluminum pipe is designed, analyzed and produced. To this end, first, a new resonant structure is designed and then, utilizing the Bloch-Floquet theorem and assuming a periodic distribution of the resonant cells through the pipe, the effects of these resonators on the structure are investigated.…”