Analysis of flexural and torsional vibration band gaps in phononic crystal beam

Phononic crystals (PCs) play an important role in the reduction of vibration within a targeted frequency range. Most research of the one-dimensional PCs focuses on the properties or applications of the flexural band gaps; however, practically, the broadband environmental excitations also induce the torsional vibration. Hence, this paper studies a two-degrees-of-freedom local resonance (2DOF-LR) phononic crystal, which can both suppress the propagation of flexural and torsion waves in the same frequency range. To improve the computational efficiency, the Timoshenko theory with a modified transfer matrix (MTM) approach is used for flexural vibration band structure analysis. Through the finite element method (FEM), the vibration attenuation characteristics of the structure within the band gaps are verified. A comprehensive study is conducted to investigate the effects of geometric and material parameters on the attenuation characteristics of the phononic crystal. Finally, a prototype of the proposed phononic crystal is fabricated for the vibration experiment. It is worth noting that a novel experimental setup using the lever principle is designed in this paper to verify the torsional band gap. The frequency ranges of the experimental vibration attenuation match well with the numerical results.