Linear dynamic analysis of axially moving cylindrical nanoshells considering surface energy effect with constant velocity

Due to the increasing advances in nanoscience and the development of technologies for making nanostructures, their application in various industries is expanding. Therefore, careful study and recognition of their dynamic behavior for proper design and application are very important. The behavior of axially moving simply supported cylindrical nanoshells in terms of dynamic stability and linear free vibrations will be investigated in this paper by considering the effect of surface stress at constant velocity. In this study, the Gurtin–Murdoch theory of surface elasticity is used to consider the surface effect. To obtain the linear governing equations, Love's shell theory is used in the framework of the theory of surface elasticity. Eventually, the final equations are derived using Hamilton's principle. Then, the partial governing equations of the nanoshell are transformed into time-dependent equations by using the Galerkin method and MAPLE software. The eigenvalues associated with linear differential equations are obtained after using the steady state method. Finally, the results are presented in the form of temporal and frequency responses to investigate the effects of nano dimensions, velocity changes, surface parameters such as surface density, residual stress and surface Lamé parameters and geometric parameters such as thickness, radius to thickness ratio and length to radius ratio on the system's dynamic behavior.