Thermo-mechanical nonlinear vibration in nano-composites polyethylene shell reinforced by CNT's 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,  . Employing nonlinear terms of strains-displacements based on Donell's theory, stress-strain relation, first order shear deformation theory and Hamilton's principal, the governing equations were obtained. 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 .