The effects of the viscosity and density on the natural frequency of the cylindrical nanoshells conveying viscous fluid

Abstract

In the present paper, the mechanical interaction between a cylindrical nanoshell and the surrounding fluid is investigated with considering small scale effects based on nonlocal elasticity theory. The Navier–Stokes equations are applied to model the external force between viscous fluid and nanoshell. The mechanical analysis of the cylindrical nanoshell which is immersed by several viscous fluids is studied to investigate the influences of the viscosity and density of the fluids on vibration characteristics of the cylindrical nanoshell. First-order shear deformation theory is applied to consider the shear effects. The governing differential equations of motion are obtained based on Hamilton’s principle for simply support boundary conditions. The effects of several parameters including nonlocal parameter, viscosity of fluids and geometrical properties are investigated on the natural frequency of the cylindrical nanoshells. Numerical results reveal that the viscosity and density of the fluids have considerable influences on the natural frequency of the cylindrical nanoshells.