基于声子晶体理论的弹性地基梁的振动特性研究  

Research on the Vibration Property of the Beam on Elastic Foundation Based on the PCs Theory

作　　者：陈启勇[1] 胡少伟[1,2] 张子明[1] 

机构地区：[1]河海大学力学与材料学院,南京210098 [2]南京水利科学研究院材料结构所,南京210029

出　　处：《应用数学和力学》2014年第1期29-38,共10页Applied Mathematics and Mechanics

摘　　要：荷载影响结构的振动特性,引起抗振性能的变化.借助声子晶体理论,研究弹性地基梁的带隙特性,建立了轴向力作用时Winkler地基上声子晶体Euler梁弯曲振动模型,采用改进的传递矩阵法,计算出梁的能带结构,判断出能带结构的变化趋势.研究表明,轴力改变能带结构,带隙范围发生变化.拉力提升带隙,但地基带隙保持不变;压力降低带隙频率,地基带隙随着压力的增加而减小.同时,进行Euler模型的数值模拟,仿真的结果与理论值基本吻合.通过轴力可以调节带隙的频率范围,达到抗振、减振的效果.Axial loads imposed on the structure influence the vibration properties and cause the change of vibration resistance functions. Theory about the band gap properties of phononic crystals （PCs） were used to study the flexural vibration band gaps of an Euler beam on elastic foundation. A flexural vibration model of the infinite periodic PCs Euler beam was established, which was under the actions of axial force and Winkler foundation. A modified transfer matrix （MTM） method was applied to calculate the band structure of the beam. The change tendency of the band structure were estimated on the basis of the band structure. Results show that axial loads influence the band gaps and band frequency ranges. Axial tensile loads elevate the band gap frequencies, but the base band gaps remain unchanged; axial compressive loads lower the band gap frequencies, and the base band gap frequencies drop when the amplitudes of the com- pressive loads increase. Meanwhile, the Euler beam model was numerically simulated, and the results were matched with the analytical ones. Through adjusting the magnitude of the axial loads, different band frequency ranges and effects of vibration reduction could be achieved.

关 键 词：声子晶体 弹性地基梁 带隙 

分 类 号：O422.6[理学—声学]