利用传递矩阵法并结合Bloch定理,分析了周期性Euler梁在Winkler地基上的弯曲振动能带结构,以及地基参数、结构参数对弯曲振动带隙的影响。结果表明,Winkler地基的存在,使得周期性Euler梁的弯曲振动能带结构向高频方向提升,第1弯曲振动带隙从0Hz开始,且随着地基反应模量的增加,第1弯曲振动带隙宽度增大,第2弯曲振动带隙宽度减小;随着长度率的增加,梁的第1弯曲振动带隙和第2弯曲振动带隙宽度均减小。与均质Euler梁对比,周期性Euler梁在Winkler地基上具有更好的隔振特性,对低频弯曲振动有较好的阻隔效果。

Periodic Euler beam has flexural vibration band gap characteristics. In order to study the flexural vibration band gap features of the periodic Euler beam on the Winkler foundation, the transfer matrix method and Bloch theorem are used to calculate the vibration band structure and analyze the impact of the parameters of foundation and structure on the band gaps. The results show that the existence of Winkler foundation makes vibration band gaps trend to higher frequency, and a new band gap that starts at 0 Hz appears in the case of having a foundation. Additional results demonstrate that with increasing the foundation reaction modulus, the range of the 1st band gap becomes wider and the range of the 2nd band gap becomes narrower. Along with the increase of the length ratio, the range of the 1st band gap and the 2nd band gap both become narrower. Compared with the homogeneous Euler beam, periodic Euler beam has better vibration isolation characteristics at low frequency.