Exact Size-Dependent Elasticity Solution for Free Radial Vibration of Nano-Sphere

Abstract

An exact size-dependent elasticity solution based on surface energy theory is used to investigate the free radial vibration behavior of a nanoscale sphere. The Gurtin-Murdoch surface elasticity model is employed to incorporate surface stress terms into pertinent boundary conditions. This leads to frequency equations involving spherical Bessel functions. Extensive numerical calculations have been carried out to illustrate the size effect of the nano-sphere on the first and second dimensionless breathing natural frequencies. The numerical results describe the imperative influence of surface energy and radii ratio on the vibrational characteristic frequency of the nano-sphere. In particular, the surface energy is much more important when the inner radius is smaller than 50 nm.