Nonlocal Shell Model for Predicting Axisymmetric Vibration of Spherical Shell-Like Nanostructures

Axisymmetric vibration of spherical shell-like nanostructures is investigated based on nonlocal elastic theory. The size effect is taken into consideration using the Eringen's nonlocal constitutive equations. A new prediction formula for the axisymmetric vibration of nano-spherical membrane shell, including small scale effect, is presented by employing Legendre and associated Legendre polynomials. The suggested model is justified by good agreement between the results given by the present method and available experimental and numerical results. This model is used to predict the axisymmetric vibration of two types of the spherical shell-like nanostructures. They include spherical fullerenes and empty spherical viruses.