Study On Band Gap Of Acoustic Metamaterial Plate With Self-similar Structure

Acoustic metamaterial is a compound structure with band gap. It blocks elastic waves within the certain frequency range, making it widely researched in the field of sound insulation and noise reduction. The thesis carried out the partical research for acoustic metamaterial’s band gaps.The thesis analyzed bang gap’s change rules of unit cell of the locally resonant acoustic metamaterial plate, through theoretical analysis and simulation calculation,based on the vibration absorber principle. First, the thesis proposed the simplified model of acoustic metamaterial plate and deduced bending vibration equation according to the theory of thin plate bending vibration. Through MATLAB calculated the structural dispersion relation, and the antiphase resonance frequency obtained by simulation within the band gap range, which verified the correctness of the result.Mass and the membrane initial deformation are the main influencing factors of structural vibration characteristics. The thesis got the structural dispersion relation and found that, in order to achieve the structural broadband and low-frequency, the quality of the mass and the initial deformation of the membrane must be controlled within a reasonable range. Then, the thesis further analyzed the change conditions of Bragg scattering and local resonance mechanisms for acoustic metamaterial plate without mass, given the corresponding range of material parameters.Considering the existence of mass helps to realize the acoustic metamaterial plate low-frequency broadband band gap characteristics, the thesis constructed the different self-similar models by increasing ring to research the broad gap characteristics. The results showed that the increase of mass makes the acoustic metamaterial plate band gap become wider frequency band, the center frequency reduced, the number of band gap increase, narrow ring mass can obtain wider band gap than wide ring mass. Sound of self-similar structure vibration response analysis found that the displacement of the mass is greater than other areas in the first resonance, at this time the mass absorbs most of the energy in the process of vibration; in the second resonance, the displacement of the mass and border is small,the internal ring and membrane vibration energy increase; the increase of ring mass is advantageous to the structure of energy evenly distributed. The transfer function of multiple composite plate structure is given by comparing the transmission pressure and incident sound pressure. Studies have shown that the more combination number, the absolute transfer function value is larger; the distancebetween the acoustic metamaterial plate influence on transfer function is similar to the sine function change rule; transfer function can obtain ideal value when the number of combinations and the distance between the two plate only within the suitable range, which provides reference frame for the acoustic detection.