Effect of surface stress and surface mass on elastic vibrations of nanoparticles

The elastic vibrations of nanoparticles, in the present work, have been studied theoretically by taking into account the size-dependent elasticity due to the surface effect. Surface elasticity has been resorted to where, in addition to the effect of surface stress, the effect of surface mass has also been taken into account in the model. The torsional and spherical modes for the free vibration have been obtained. Numerical calculations have been conducted, and the results have shown that both the surface stress and the surface mass affect significantly the eigenfrequencies of nanospheres. With those surface effects, the eigenfrequencies are no longer proportional to the radius inverse. Under appropriate circumstances, the surface effects may render the lowest eigenfrequency amount to the second lowest by classical elasticity.