Attenuation properties of a meta-pipe: Analytical, experimental, and numerical prediction

Flexural vibration characteristics of a meta-pipe are investigated in this paper. Initially, the metamaterial piping system consisting of a homogeneous pipe and periodic flexible supports is designed. Subsequently, the dispersion relationship which is a function of the wavenumber and the frequency is derived employing the transfer matrix method and Bloch’s theorem. The designed system reveals a zero-frequency stopband and a wide passband in the examined frequency range, which are verified by both experimental and numerical results. To enhance the performance of this system, it is essential to effectively control the obtained passband. For this, a single-degree-of-freedom localized resonator is designed, which is subsequently installed at the center of each unit-cell of the pipe. The dispersion properties of this system are first evaluated analytically and then validated using experimental and numerical methods. Finally, the effect of pipe system parameters and resonator properties on the stopband characteristics is studied in depth. It was observed that the stopband properties can be effectively tuned by appropriately designing the piping system and resonators. The results presented in this study offer valuable insights into the propagation characteristics of flexural waves and the strategies devised for controlling vibrations in pipes.