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基于非局部理论的黏弹性纳米杆轴向振动与波传播研究

唐光泽 姚林泉 李成 季长剑

唐光泽, 姚林泉, 李成, 季长剑. 基于非局部理论的黏弹性纳米杆轴向振动与波传播研究[J]. 应用数学和力学, 2019, 40(1): 36-46. doi: 10.21656/1000-0887.390166
引用本文: 唐光泽, 姚林泉, 李成, 季长剑. 基于非局部理论的黏弹性纳米杆轴向振动与波传播研究[J]. 应用数学和力学, 2019, 40(1): 36-46. doi: 10.21656/1000-0887.390166
TANG Guangze, YAO Linquan, LI Cheng, JI Changjian. Longitudinal Vibration and Wave Propagation of Viscoelastic Nanorods Based on the Nonlocal Theory[J]. Applied Mathematics and Mechanics, 2019, 40(1): 36-46. doi: 10.21656/1000-0887.390166
Citation: TANG Guangze, YAO Linquan, LI Cheng, JI Changjian. Longitudinal Vibration and Wave Propagation of Viscoelastic Nanorods Based on the Nonlocal Theory[J]. Applied Mathematics and Mechanics, 2019, 40(1): 36-46. doi: 10.21656/1000-0887.390166

基于非局部理论的黏弹性纳米杆轴向振动与波传播研究

doi: 10.21656/1000-0887.390166
基金项目: 国家自然科学基金(11572210);江苏省研究生科研与实践创新计划项目(KYCX17_1983)
详细信息
    作者简介:

    唐光泽(1994—),男,硕士生(E-mail: 20164246007@stu.suda.edu.cn);姚林泉(1961—),男,教授,博士,博士生导师(通讯作者. E-mail: lqyao@suda.edu.cn).

  • 中图分类号: O346

Longitudinal Vibration and Wave Propagation of Viscoelastic Nanorods Based on the Nonlocal Theory

Funds: The National Natural Science Foundation of China(11572210)
  • 摘要: 根据非局部理论和Kelvin黏弹性理论,针对黏弹性纳米杆自由振动和波传播的轴向动力学问题进行研究.首先,推导了黏弹性纳米杆的轴向动力学微分控制方程.然后,通过无量纲化讨论了3种典型边界纳米杆的前三阶振动特性.最后,研究黏弹性纳米杆波的传播问题,导出了圆频率、波速与波数之间的关系.数值结果表明,非局部效应使第一、二阶固有频率持续减小,第三阶频率先增大再减小,出现结构刚度削弱和增强两种趋势.特别地,对于自由端存在集中质量的情形,第二阶频率随着黏性系数增大出现了多值情况,易导致杆件失稳.数值算例还说明了非局部效应的增强可有效降低黏性材料的阻尼效应,产生逃逸频率,使得纵波能够在高波数段传播.另外,黏性系数在低波数段对阻尼比影响可忽略不计,而在高波数段下,黏性系数越大则阻尼比越大.
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出版历程
  • 收稿日期:  2018-06-14
  • 修回日期:  2018-07-21
  • 刊出日期:  2019-01-01

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