分数导数粘弹性半无限长杆中纵波的传播  

Longitudinal Waves Propagation in Semi-infinite Bars Described by Fractional Derivative Viscoelastic Model

作　　者：闫启方[1] 刘林超[2] 

机构地区：[1]信阳师范学院土木工程学院,信阳464000 [2]上海市应用数学和力学研究所,上海200072

出　　处：《机械科学与技术》2009年第8期1087-1091,共5页Mechanical Science and Technology for Aerospace Engineering

基　　金：上海市重点学科建设项目(Y0103)资助

摘　　要：纵波在粘弹性杆中传播时会表现出弥散特性,研究分数导数粘弹性模型描述的粘弹性半无限长杆中纵波的传播具有重要的意义。利用分数导数的性质及粘弹性理论得到了分数导数粘弹性模型描述的粘弹性杆中波的相速度和衰减因子,分析了松弛时间和分数导数微分算子的阶数对相速度和衰减因子的影响规律。Longitudinal waves display dispersion properties when they propagate in viscoelastic bars. It is important to study the propagation of longitudinal waves in semi-infinite bars described by fractional derivative viscoleastie model. We obtained phase velocity and attenuation factor of waves in semi-infinite bar described by fractional derivative viscoleastic model by using the properties of fractional derivative and viscoelastic theory, and analyzed the influence of relaxation time and order of fractional differential operator on phase velocity and attenuation.

关 键 词：粘弹性杆 相速度 衰减因子 分数导数 弥散特性 

分 类 号：TU311.1[建筑科学—结构工程]