Nonlinear dynamic response of functionally graded cylindrical microshells conveying steady viscous fluid

Abstract

Nonlinear free and forced vibrations for functionally graded (FG) cylindrical microshells conveying steady viscous fluid are investigated based on the shear deformation shell and potential flow theory. The size effects are considered by modified couple stress theory. Steady viscous force produced by fluid are added to the inviscid and incompressible microshell-fluid coupled system using time-mean Navier-Stokes equations. Using Hamilton’s principle, the nonlinear partial differential equations are derived for microshell-fluid system. The reduced nonlinear ordinary differential equations are obtained based on static condensation method and Galerkin’s method. The critical flow velocity and natural frequency are here discussed by changing material composition and scale parameters. Moreover, the effects of axial load, scale parameter, fluid flow velocity and viscosity on nonlinear dynamic response are also investigated. Comparisons with corresponding inviscid case and previously literatures are also here discussed