Abstract
The grid structure is widely used in architectural and mechanical field for its high strength and saving material. This paper will present a study on an acoustic metamaterial beam (AMB) based on the normal square grid structure with local resonators owning both flexible band gaps and high static stiffness, which have high application potential in vibration control. Firstly, the AMB with variable cross-section frame is analytically modeled by the beam–spring–mass model that is provided by using the extended Hamilton’s principle and Bloch’s theorem. The above model is used for computing the dispersion relation of the designed AMB in terms of the design parameters, and the influences of relevant parameters on band gaps are discussed. Then a two-dimensional finite element model of the AMB is built and analyzed in COMSOL Multiphysics, both the dispersion properties of unit cell and the wave attenuation in a finite AMB have fine agreement with the derived model. The effects of design parameters of the two-dimensional model in band gaps are further examined, and the obtained results can well verify the analytical model. Finally, the wave attenuation performances in three-dimensional AMBs with equal and unequal thickness are presented and discussed.
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