Flexural wave mitigation in metamaterial cylindrical curved shells with periodic graded arrays of multi-resonator

This paper aims to present a theoretical model of flexural wave bandgaps in locally resonant cylindrical curved shell and investigates a technique for broadband wave mitigation using a metamaterial cylindrical curved shell. Firstly, cartesian coordinates are converted to cylindrical coordinates in the cylindrical curved shell structure to construct periodic conditions in the circumferential direction. Then, governing equations are derived by using the extended Hamilton principle, and plane wave expansion (PWE) method is implemented to calculate the band structures of acoustic metamaterial cylindrical curved shells with different multi-resonator parameters. In addition, a periodic graded arrays technique is also utilized to broaden the frequency range of bandgap. Lastly, finite element method (FEM) is used to calculate the band structures and vibration transmission characteristics to verify the accuracy of PWE results. The results disclose that the proposed structure has a good attenuation effect on flexural wave and the periodic graded arrays technique can effectively splice bandgaps of each resonator to enlarge frequency range of the flexural wave mitigation. Hence, the proposed structure can be used to achieve a good attenuation effect on flexural wave in the future.