Nonlinear bending and vibration of FGCNTs cylindrical microshells conveying microfluid under a 2D magnetic field

Abstract

This paper presents the nonlinear static bending and nonlinear dynamic analysis of cylindrical microshells conveying microfluid and exposed to a 2D magnetic field. The composite shell is made of a polymer matrix reinforced with functionally graded (FG) carbon nanotubes (CNTs). The CNT dispersion varies across the shell thickness according to a power law. Four types of CNT distributions are examined. To account for the small-size effect using a single material parameter, the modified couple stress theory is applied. Additionally, the small-size effect of the microfluid is considered using the Knudsen number. To model fluid–structure interaction, the Navier–Stokes equation for magnetic-fluid flow is employed. The nonlinear motion equations of the cylindrical microshells conveying fluid are developed using Hamilton’s variational principle. The Galerkin approach is used to convert the motion equations into an algebraic system for static bending and into ordinary differential equations (ODEs) for dynamic analysis. The ODEs are solved using the fourth-order Runge–Kutta method. Numerical results reveal the positive role of fluid flow, CNT reinforcement, and magnetic field on the structural behavior of cylindrical microshells. Furthermore, considering the small-size effects of the structure and fluid leads to a noticeable reduction in the amplitude of the deflection waves.