摘要
研究了非局部理论下纳米杆件纵向振动的尺度效应,根据分析力学得到了振动的偏微分控制方程,采用分离变量法探讨了杆件在三种边界条件下的振动特性.结果表明:微尺度效应使得纳米杆振动固有频率降低,经典力学高估了小尺度下杆件振动的固有频率,并且无量纲化尺度参数越大或模态阶数越高,频率降低越快.两端固支与两端自由纳米杆的固有频率形式相同,这与宏观连续介质力学结论也一致.特别地,还考虑了自由端存在质量集中的纳米杆动力学行为.同时给出了算例,具体量化了尺度效应的影响程度,并初步探讨了不同应变类型下,控制方程形式的不同及其所带来的解的变化.
The size effects in longitudinal dynamics of nano-poles are investigated using nonlocal theory.A partial differential governing equation is obtained based on analytical mechanics and the vibration properties under three kinds of boundary conditions are studied via the method of separation of variables.It is shown that micro-scale effects make the natural frequency lower than classical mechanics.The classical mechanics overestimates natural frequency of micro-scale longitudinal vibration,and the frequency decreases faster with a higher dimensionless scale parameter or a higher vibration mode.Natural frequencies of fixed-fixed and free-free nano-poles are the same and it is consistent with macro classical mechanics. In particular,dynamic properties of a fixed-free nano-pde with concentrated mass at its free end are also presented. Numerical examples are presented and they quantify the size effects.Different governing equation that employs different form of strain is also analyzed and discussed.
出处
《苏州大学学报（自然科学版）》
CAS
2012年第3期37-42,共6页
Journal of Soochow University(Natural Science Edition)
基金
苏州大学引进人才科研启动项目(Q413300511)
关键词
纵向动力学
微尺度效应
纳米杆
固有频率
longitudinal dynamics
micro-scale effects
nano-pole
natural frequency
