基于非局部理论的压杆稳定性及轴向振动研究

根据非局部弹性理论，研究压杆稳定性和弹性杆件轴向振动问题。结合三种典型边界条件，推导临界压力及固有频率非局部理论解。该显式解表明，无量纲小尺度参数的增大会使临界压力及固有频率减小。由压杆稳定性算例结果显示，非局部临界压力随着压杆长度的增加而减小，当压杆长度接近宏观尺寸时，临界压力趋于稳定。与经典连续介质力学相比，非局部临界压力及固有频率降低，说明经典力学高估小尺度下压杆受压承载能力及结构振动频率，随着压杆长度的增加，经典解与非局部解趋于一致。

On the stability and axial vibration of compressive bars based on nonlocal elasticity theory

The stability and axial vibration of a compressive bar are investigated through the nonlocal elasticity approach. The explicit solutions for critical pressure and inherent frequency are obtained according to three typical kinds of boundary conditions. It is shown that an increase in dimensionless small scale parameter causes the critical pressure and inherent frequency to decrease. A numerical example is presented and it indicates the nonlocal critical pressure decreases with increasing the length of compressive bars, and critical pressure approaches to a constant when the length is closed to macro size. Nonlocal critical pressure and inherent frequency are lower than the results from classical continuum mechanics, namely, the classical mechanics overestimates the critical pressure and inherent frequency of a structure at small scale. With an increase in length of the compressive bars, nonlocal results are in good agreement with classical results.