Vibration analysis of fluid-conveying multi-scale hybrid nanocomposite shells with respect to agglomeration of nanofillers

Abstract

The vibration problem of a fluid conveying cylindrical shell consisted of newly developed multi-scale hybrid nanocomposites is solved in the present manuscript within the framework of an analytical solution. The consistent material is considered to be made from an initial matrix strengthened via both macro- and nano-scale reinforcements. The influence of nanofillers’ agglomeration, generated due to the high surface to volume ratio in nanostructures, is included by implementing Eshelby-Mori-Tanaka homogenization scheme. Afterwards, the equivalent material properties of the carbon nanotube reinforced (CNTR) nanocomposite are coupled with those of CFs within the framework of a modified rule of mixture. On the other hand, the influences of viscous flow are covered by extending the Navier-Stokes equation for cylinders. A cylindrical coordinate system is chosen and mixed with the infinitesimal strains of first-order shear deformation theory of shells to obtain the motion equations on the basis of the dynamic form of principle of virtual work. Next, the achieved governing equations will be solved by Galerkin’s method to reach the natural frequency of the structure for both simply supported and clamped boundary conditions. Presenting a set of illustrations, effects of each parameter on the dimensionless frequency of nanocomposite shells will be shown graphically.

Keywords

• Vibration
• Agglomeration effect
• Multi-scale hybrid nanocomposites
• Galerkin’s solution
• Viscous fluid flow