周期结构带隙的能效观点  

Study on the Band-gap of Periodic Structures in the Viewpoint of Power Efficiency

作　　者：周俊[1] 饶柱石[2] 塔娜[2] 

机构地区：[1]上海交通大学振动冲击噪声研究所,上海200240 [2]上海交通大学机械系统与振动国家重点实验室,上海200240

出　　处：《噪声与振动控制》2016年第2期1-5,45,共6页Noise and Vibration Control

基　　金：国家重点基础研究发展计划资助项目(2014CB046302)

摘　　要：在几何构型或材料特性方面具有空间重复特性的一类结构,称为周期结构,如桁架、加强筋板等。在一定频率范围内,周期结构能够阻断弹性行波在其中传递,该特性可应用于隔振器开发。现有周期结构隔振分析大多基于无限长假设,即假设周期结构在几何空间中可无限延伸,因此只有行波解具有物理意义,非行波模式则被忽略。然而,工程中隔振系统都是有限长的,因此非行波解的确存在,故其能量传输特性具有研究价值。周期桁架有限元数值仿真结果表明,周期结构行波解的功率因数始终等于1,说明频散曲线与能量传输效率有关。据此引入效率指标函数,通过其响应表面局部极大值、极小值的连线,将频率-波数空间划分为能量传输高效区和低效区。该划分方式能统一处理行波解和非行波解的情况,拓展原有带隙分析适用范围,为有限周期结构能量传输效率分析提供新途径,对于隔振器开发设计具有重要参考价值。Periodic structure is the repetitive in geometric configurations or material properties, such as trusses and rib-stiffened plates. In certain frequency bands, periodic structure can isolate the incident travelling waves. This property is widely applied in vibration isolator’s design. Generally, the analysis of periodic structure’s attenuation property is always based on infinite length assumption. It means that the periodic structure can extend infinitely in space. So, only travelling wave solutions have physical significance and the non-travelling wave solutions are neglected. However, the periodic structure in engineering is finite and the non-travelling wave solutions exist indeed. Therefore, the investigation of their power transfer properties is of significance. The finite element simulations of the periodic truss show that the power factor of the travelling wave solution is always equal to unity. It means that the dispersion curves are related to power transfer efficiency. Hence, the efficiency index function is introduced. According to the local maximum and minimum values of the index function’s response surface, the frequency-wave number space can be divided into a series of high efficiency and low efficiency transfer regions. This method can be applied to both traveling and non-traveling wave solutions. The method extends the scope of band-gap analysis and gives an alternative approach for finite periodic structure’s power transfer analysis. The results of the present work are of significance for vibration isolator’s development.

关 键 词：振动与波 周期结构 功率因数 效率 带隙 桁架 

分 类 号：O328[理学—一般力学与力学基础] TB535[理学—力学]