Nonlocal elasticity theory for radial vibration of nanoscale spherical shells

• Propose the nonlocal shell model for predicting the radial vibration of nanoscale spherical shells.
• The influence of small scale on the frequencies of the nanoscale spherical shells is investigated.
• The relation between the nonlocal and local frequencies is developed.

This paper presents the radial vibration of nanoscale spherical shells based on the nonlocal elasticity theory. The shell is considered elastic, homogeneous and isotropic. The nonlocal differential equation of radial motion is derived in terms of radial displacement. The relation between the nonlocal and local frequencies is also investigated. Considering the small-scale effect, the general characteristic equation for radial vibration of spherical shell is obtained by applying boundary conditions. Moreover, the characteristic equations for two special cases are presented. To demonstrate the accuracy of the present formulation, theoretical calculations of the fundamental frequency have been compared with those available in the literature and a good agreement is achieved. The variations of the frequencies with the nonlocal parameter, radius ratio and Poisson's ratio are also examined. It is observed that the frequencies are affected when the size effect is taken into consideration.