一维粘弹材料周期结构的振动带隙研究

RESEARCH ON THE VIBRATION BANDGAPS OF ONE DIMENSIONAL VISCOELASTIC PERIODIC STRUCTURE

采用迭代法改进了一维声子晶体带隙特性计算的平面波展开(PWE)算法,以使其适用于组成材料粘弹性所导致的弹性常数随频率非线性变化的特性。将该算法应用于丁腈橡胶(NBR)和钢组成的两种结构尺寸的一维周期结构声子晶体振动带隙的研究中,理论计算和振动测试结果吻合理想。进一步的理论分析表明,橡胶材料的储能弹性模量随频率的单调增加,使得在保持禁带开始频率不变的同时大大加宽了禁带范围,在3 mm钢/10 mm NBR以及7 mm钢/10 mm NBR两种周期结构一维声子晶体中禁带宽度分别增加了36.4％和34.0％。

The one dimensional plane wave expansion (PWE) algorithm is improved using iterative method in order to solve the problem of nonlinear changing of elastic constants with frequency, which is found in calculating of the band gaps of one dimensional viscoelastic phononic crystals. The new method is applied in the research of the vibration band gap of one dimensional steel/butadiene acrylnitrile rubber (NBR) periodic structure. The calculation results are in good agreement with the experimental results. Further theoretical analyses shows that the nonlinear changing of elastic constants with frequency of viscoelastic rubber can remarkably increase the width of first band gap, and at the same time hold the starting frequency of it. For the two cases, the width of first band gap increased by 36.4% (for the 3 mm steel/10 mm NBR periodic structure) and 34.0% (for the 7 mm steel/10 mm NBR periodic structure) respectively.