A metamaterial cylindrical shell with multiple graded resonators for broadband longitudinal wave attenuation

This paper investigates a metamaterial cylindrical shell with local resonators for broadband longitudinal wave attenuation. A three-component phononic crystal metamaterial cylindrical shell that opens local resonant bandgaps at low frequencies is formed by periodically inserting a lead column coated with soft rubber into an ordinary cylindrical shell. First, the governing equations of elastic wave propagation in cylindrical shell structures are derived through coordinate transformation. Subsequently, numerical models of the metamaterial cylindrical shell are established, and the dispersion relation and vibration transmission characteristics of this structure are calculated using the Finite Element Method (FEM). Finally, in order to further broaden the bandgaps and the strong suppression range of the structure, a multiple-graded-resonator metamaterial cylindrical shell with three different local resonators is also proposed. These local resonators have different start frequencies and locations of their longitudinal wave bandgaps, so they can be combined to produce a wider overall bandgap. Numerical results show that this kind of multiple-graded-resonator metamaterial cylindrical shell has a good vibration suppression effect on longitudinal waves in the range of approximately 180–710 Hz and the vibration suppression effect can reach −40 dB at best. In addition, experimental results on vibration transmission characteristics show good agreement with the numerical results. This work provides a new idea and method for the development of acoustic metamaterials to obtain broadband and low-frequency bandgaps for cylindrical shell structures.