| A Continuum mechanics model for the study and analysis of free vibrations of nanoparticles having isotropic symmetry and under free boundary conditions is carried out. The nanoparticles are considered to be continuous solids. Hamilton's principle is used to obtain the weak form of the partial differential equations governing the problem and then the Ritz method based on power series for the approximation functions is used to solve the corresponding eigenvalue problem. The proposed continuum mechanics model was applied to two different geometries, cubic and spherical, and to three different materials, silicon, carbon, and germanium. The resulting natural frequencies are compared to frequencies obtained from a molecular dynamics analysis. The main goal was in some degree to validate and to set the limitations of the continuum mechanics approach when dealing with very small length scales. |
