Small-scale effects on the radial vibration of an elastic nanosphere based on nonlocal strain gradient theory

Nonlocal strain gradient theory is widely used when dealing with micro- and nano-structures. In such framework, small-scale effects cannot be ignored. In this paper a model of radial vibration of an isotropic elastic nanosphere is theoretically investigated. The frequency equation is obtained from a nonlocal elastic constitutive law, based on a mix between local and nonlocal strain. This model is composed of both the classical gradient model and the Eringen's nonlocal elasticity model. To check the validity and accuracy of this theoretical approach, a comparison is made with the literature in certain specific cases, which shows a good agreement. Numerical examples are finally conducted to show the impact of small-scale effects in the radial vibration, which need to be included in the nonlocal strain gradient theory of nanospheres. It reveals that the vibration behavior greatly depends on the nanosphere size and nonlocal and strain gradient parameters. Particularly, when the nanospheres radius is smaller than a critical radius, the small-scale effects play a key role. Thus, the obtained frequency equation for radial vibration is very useful to interpret the experimental measurements of vibrational characteristics of nanospheres.