细直梁弯曲振动中的局域共振带隙

通过将声子晶体中的局域共振思想引入到细直梁的结构设计中,构造了一种具有低频局域共振带隙的周期结构细直梁。采用传递矩阵法计算了周期边界条件下该细直梁弯曲振动中的弹性波能带结构,计算结果表明该结构中存在低频弯曲振动带隙。采用有限元法计算了有限周期该细直梁的振动传输特性。以有机玻璃、橡胶/铜块振子构成的该局域共振细直梁为例,采用振动试验方法对其振动传输特性进行了测试。试验结果同理论及仿真结果相吻合。结果表明,局域共振结构可大大降低带隙频率,并增大带隙衰减。梁类结构是噪声及振动控制领域研究的主要对象之一,局域共振结构的应用为其提供了一种新的思路。

LOCALLY RESONANT ELASTIC WAVE BAND GAPS IN FLEXURAL VIBRATIONS OF SLENDER BEAMS

The flexural vibration behavior of elastic wave across a slender beam with locally resonant structures is studied by using the transfer-matrix (TM) method and the finite element (FE) method. Flexural elastic wave band gaps are found in this locally resonant beam with its band structure calculated with the TM method. The corresponding frequency response function of a finite sample composed of organic glass beam; caoutchouc and copper blocks are calculated with FE method. Those theoretical results are verified with the vibration experiment. The calculated and measured results show a good agreement. The existence of low-frequency band gaps in the locally resonant structure provides a new way in the flexural vibration control of beams.