Beam-type acoustic metamaterial design for vibration suppression with structural damping

Abstract

Vibration suppression of a beam-type acoustic metamaterial with periodic cavities filled by a viscoelastic membrane that supports a hollow mass still filled by a viscoelastic membrane that supports a local resonator is investigated. First, the proposed beam-type acoustic metamaterial is modeled as a one-dimensional mass-in-mass-in-mass (MMM) lumped parameter chain with structural damping, and then a mass-in-mass (MM) lumped parameter chain with structural damping is also given for comparison. For the two chains, the influence of structural damping on band structures are considered, and the loss factors associated with all propagating Bloch modes are compared. Finally, as an example, the beam-type metamaterials based on MM model with structural damping and MMM model with structural damping are designed to suppress vibration, respectively. The viscoelastic membranes act as structural damping. The finite element method based on Kirchhoff's plate theory is developed to capture dynamic displacement fields of different metamaterials. Structural frequency response is calculated for different configurations of cantilevered structures when disturbance is considered. The results show that the proposed beam-type acoustic metamaterial based on MMM model with structural damping has higher dissipation and display high damping and does not sacrifice stiffness than MM model with structural damping.