Thermo-Mechanical Nonlinear Vibration in Nano-Composites Polyethylene Shell Reinforced by CNTʹʹs Embedded Elastic

In this study, thermo-mechanical nonlinear vibration of a polyethylene (PE) cylindrical shell embedded in an elastic foundation was investigated. The shell is reinforced by armchair Carbon nanotubes (CNTs) where characteristics of the equivalent composite being determined using Mori-Tanaka model. The elastic medium is simulated using the spring constant of the Winkler-type. The governing equations were obtained by employing nonlinear terms of strains-displacements based on Donellʹs theory, stress-strain relation, first order shear deformation theory and Hamiltonʹs principal. Differential quadrature method (DQM) is used to calculate the nonlinear frequency of the shell. The influences of geometrical parameters, orientation angle of CNTs and elastic foundation constants on the nonlinear vibration of the shell were investigated. Results showed that the nonlinear effect represented by nonlinear frequency ratio is considerable at lower .