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采用集中质量法对一维三组元杆状结构声子晶体带隙特征进行计算,将其与一维二组元杆状结构声子晶体进行比较。研究表明,一维三组元结构声子晶体能有效拓宽带隙频率范围且能降低起止频率。在一维二组元(铝/塑料)声子晶体组份材料铝和塑料之间插入丁腈橡胶前后,保证2个模型的晶格常数a=0.3m、自由度总数300相同。当组份比t为1时,三组元(铝/丁腈橡胶/塑料)声子晶体可以降低第1带隙的起始频率463.7Hz、截止频率2 108.1Hz。当三组元声子晶体晶格常数a由0.03m增大到0.42m时,该声子晶体第1带隙起始频率由18 943Hz下降到1 353.1Hz,截止频率由37 799Hz下降到2 699.9Hz。如果取三组元声子晶体的晶格常数为0.3m,固定其中铝的长度为0.15m,将丁腈橡胶和塑料的长度之和固定为0.15m,调节丁腈橡胶的长度由0m增大到0.15m时,该声子晶体第1带隙起始频率由2 359.8Hz下降到1 664.7Hz,截止频率由5 888.0Hz下降到4 065.3Hz。同时该声子晶体第1带隙宽度变化在低频率区存在一个峰值3 043.6Hz。这些变化规律对拓展一维杆状声子晶体的带隙特征具有积极意义。
The bandgap characteristics of one-dimensional three-component rod-shaped phononic crystals were calculated by the method of mass concentration, and compared with one-dimensional two-component rod-shaped phononic crystals. The results show that one-dimensional three-element phononic crystals can effectively broaden the band gap frequency range and reduce the starting and ending frequencies. In the one-dimensional two-component (aluminum / plastic) phononic crystal component material before and after the insertion of nitrile rubber between aluminum and plastic, to ensure that the two models lattice constant a = 0.3m, the total number of 300 degrees of freedom the same. When the component ratio t is 1, the three-component (aluminum / nitrile rubber / plastic) phononic crystal can reduce the first bandgap start frequency 463.7Hz and the cutoff frequency 2 108.1Hz. When the lattice constant a of the three sets of phononic crystals increases from 0.03 to 0.42 m, the initial band gap frequency of the phonon crystal decreases from 18 943 Hz to 1 353.1 Hz and the cut-off frequency decreases from 37 799 Hz to 2 699.9 Hz. If the crystal constants of three sets of phononic crystals are taken as 0.3 m, the length of aluminum is fixed at 0.15 m, the sum of the lengths of nitrile rubber and plastic is fixed at 0.15 m, and the length of nitrile rubber is adjusted from 0 m At 0.15m, the first bandgap frequency of the phononic crystal drops from 2 359.8Hz to 1 664.7Hz, and the cut-off frequency decreases from 5888.0Hz to 4065.3Hz. At the same time, the change of the first band gap width of the phonon crystal has a peak of 3 043.6 Hz in the low frequency region. These changes have a positive meaning to expand the bandgap characteristics of one-dimensional rod-shaped phononic crystals.