In this paper, based on the theory of one dimensional metamaterials beam, we present a metamaterial membrane consisting of resonance unit with periodic and one-dimensional beam structure. With the Kirchhoff plate theory , the equations of motion about the overall structure are established, and the concentrated force by mass-spring resonator and acoustic loading are calculated. By using Newton's second law and the virtual work principle, the vibration modes of different order for plate amplitude An can be computed through the equations of motion. By introducing the concept of equivalent density, the equivalent density of resonance forms is affected by plate stiffness k 、plate thickness h 、resonance unit periodic constant L and added mass M, the arbitrary affected factor is analyzed about the equivalent density peak. Within the scope of a certain size, the thickness of membrane is thinner, or the ratio between resonance unit and stiffness is smaller, the resonance frequency is lower. As the periodic constant L is larger, the resonance forms between membrane and resonance unit are coexistence, and the membrane vibration form is stronger. Finally, by discussing the resonant unit quality and transmission peak, the numerical simulation value is verified by the test results, the experiment shows the local resonance for mass-spring system has an essential role for metamaterial membrane transmission absorption.
Key words
metamaterial membrane /
resonance unit /
virtual work principle /
equivalent density /
periodic constant /
transmission peak
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References
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