School of Mechanical Engineering, Shiraz University, Shiraz, Iran.
Nanotechnology. 2013 Feb 22;24(7):075702. doi: 10.1088/0957-4484/24/7/075702. Epub 2013 Jan 28.
Radial vibration of spherical nanoparticles made of materials with anisotropic elasticity is theoretically investigated using nonlocal continuum mechanics. The anisotropic elastic model is reformulated using the nonlocal differential constitutive relations of Eringen. The nonlocal differential equation of radial motion is derived in terms of radial displacement. Cubic, hexagonal, trigonal and tetragonal symmetries of the elasticity are discussed. The suggested model is justified by a good agreement between the results given by the present model and available experimental data. Furthermore, the model is used to elucidate the effect of small scale on the vibration of several nanoparticles. Our results show that the small scale is essential for the radial vibration of the nanoparticles when the nanoparticle radius is smaller than 1.5 nm.
采用非局部连续介质力学理论研究了各向异性弹性材料制成的球形纳米粒子的径向振动。利用 Eringen 的非局部微分本构关系对各向异性弹性模型进行了重新表述。根据径向位移推导出了径向运动的非局部微分方程。讨论了弹性的立方、六方、三角和四方对称。通过将本模型给出的结果与现有实验数据进行比较，验证了所提出模型的合理性。此外，还利用该模型阐明了小尺寸对几种纳米粒子振动的影响。结果表明，当纳米粒子半径小于 1.5nm 时，小尺寸对于纳米粒子的径向振动是必不可少的。
