基于频散非局部均匀化的一维变截面声子晶体杆轴向振动特性研究  

Study on axial vibration characteristics of one-dimensional variable cross-section phononic crystal rod based on dispersion nonlocal homogenization method

作　　者：丁万玺 李小白 王兴东[1] 吴宗武[1] DING Wanxi;LI Xiaobai;WANG Xingdong;WU Zongwu(Key Laboratory of Metallurgical Equipment and Control of Ministry of Education,Wuhan University of Science and Technology,Wuhan 430081,Hubei,China;Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering,Wuhan University of Science and Technology,Wuhan 430081,Hubei,China)

机构地区：[1]武汉科技大学冶金装备及其控制教育部重点实验室,湖北武汉430081 [2]武汉科技大学机械传动与制造工程湖北省重点实验室,湖北武汉430081

出　　处：《农业装备与车辆工程》2024年第9期108-115,共8页Agricultural Equipment & Vehicle Engineering

基　　金：国家自然科学基金项目“多维耦合下非一般液体浸没的多层异质柔性带振动及微成形控制研究”(52375117);湖北省自然科学基金计划项目“基于能量等效的超构圆柱壳稳定性研究”(2022CFB632);中国博士后科学基金资助项目“基于能量等效的超构圆柱壳构性关系解析及多尺度稳定性研究”(2022M722484)。

摘　　要：以一维变截面声子晶体杆为研究对象,基于频散非局部均匀化的方法,提出并构建了一维变截面杆的等效均匀化模型。通过与有限元仿真得到的固有频率对比,验证所提模型的正确性。进一步计算不同晶格常数、周期、直径比条件下的固有频率。结果表明:变截面杆基质体积分数保持不变时,变截面杆的长度增大,等效杆的晶格常数增大,非局部效应减弱,固有频率减小;周期数目改变,不改变带宽;增强体和基质的直径比越小、带宽越小。所提方法可为变截面声子晶体杆的工程应用问题提供参考,调节结构参数还可对不同类型截面杆工程化设计提供思路。The one-dimensional variable cross-section phononic crystal rod was taken as the research object,based on the method of dispersion nonlocal homogenization,the equivalent homogenization model of one-dimensional variable cross-section rod was proposed and constructed.The correctness of the proposed model was verified by comparing with the natural frequency obtained by finite element simulation.The natural frequencies under different lattice constants,periods and diameter ratios were further calculated.The results showed that when the volume fraction of the variable cross-section rod matrix remained unchanged,the length of the variable cross-section rod increased,the lattice constant of the equivalent rod increased,the nonlocal effect weakened,and the natural frequency decreased.The number of cycles changed without changing the bandwidth;the smaller the diameter ratio of the reinforcement and the matrix,the smaller the bandwidth.The proposed method can provide a reference for the engineering application of variable cross-section phononic crystal rods,and adjusting the structural parameters can also provide ideas for the engineering design of different types of cross-section rods.

关 键 词：一维变截面声子晶体 周期杆结构 非局部均匀化方法 固有频率 带隙 

分 类 号：TB535.1[理学—物理]