Size-dependent free vibration analysis of nanoshells based on the surface stress elasticity

Based upon the Gurtin-Murdoch elasticity theory capturing the surface stress effect, a size-dependent continuum model is developed to investigate the free vibrations of nanoscale cylindrical shells. The equations of motion including the surface stress effect are derived based on the first-order shear deformation theory (FSDT) and using Hamilton's principle. A Galerkin-based closed-form solution technique together with modal beam functions is also utilized to solve the problem. Comprehensive results for the size-dependent vibration behavior of nanoshells under various boundary conditions are given. The results from the present analysis, where possible, are shown to be in very good agreement with the existing data from the literature. A comparison is also made between the predictions of surface stress model and those of its classical counterpart, and it is revealed that the surface stress has a significant influence on the resonant frequency of very thin nanoshells. Moreover, the effects of surface properties including surface elastic moduli, surface residual tension and surface mass density on the vibration characteristics of nanoshells are studied.