Dynamic stability of FG-CNT-reinforced viscoelastic micro cylindrical shells resting on nonhomogeneous orthotropic viscoelastic medium subjected to harmonic temperature distribution and 2D magnetic field

Abstract

This paper deals with the dynamic stability of embedded functionally graded (FG)-carbon nanotubes (CNTs)-reinforced micro cylindrical shells. The structure is subjected to harmonic non-uniform temperature distribution and 2D magnetic field. The CNT reinforcement is either uniformly distributed or FG along the thickness direction where the effective properties of nano-composite structure are estimated through Mixture low. The viscoelastic properties of structure are captured based on the Kelvin–Voigt theory. The surrounding viscoelastic medium is considered nonhomogeneous with the spring, orthotropic shear and damper constants. The material properties of cylindrical shell and the viscoelastic medium constants are assumed temperature-dependent. The first order shear deformation theory (FSDT) or Mindlin theory in conjunction with Hamilton\'s principle is utilized for deriving the motion equations where the size effects are considered based on Eringen\'s nonlocal theory. Based on differential quadrature (DQ) and Bolotin methods, the dynamic instability region (DIR) of structure is obtained for different boundary conditions. The effects of different parameters such as volume percent and distribution type of CNTs, mode number, viscoelastic medium type, temperature, boundary conditions, magnetic field, nonlocal parameter and structural damping constant are shown on the DIR of system. Numerical results indicate that the FGX distribution of CNTs is better than other considered cases. In addition, considering structural damping of system reduces the resonance frequency.