Nonlinear thermal instability and vibration analysis of pre/post-buckled FG porous nanotubes using nonlocal strain gradient theory

Abstract

Current research presents the nonlinear static/dynamic response of functionally graded (FG) porous nanotubes in the thermal pre- and post-buckling regimes. The case of temperature-dependent FG nanotubes with even distributed porosities subjected to uniform temperature rise is considered. The stability and vibration characteristics are analyzed for the uniformly heated nanotube surrounded by a nonlinear elastic foundation. The nonlinear equations of motion are derived using the Hamilton principle for the thermally pre/post-buckled nanotube in the framework of nonlocal strain gradient theory. The size-dependent governing equations are established based on the uncoupled thermoelasticity, the von Kármán assumption and the high-order shear deformation theory. The nonlinear governing equations are reduced for the nonlocal strain gradient-based model of nanotubes with immovable simply supported boundary conditions. The system of equations is solved for the nonlinear problems of free vibration and post-buckling of the heated tube using two-step perturbation technique and Galerkin procedure. The novel parametric examples are carried out to investigate the effect of nonlocal and length scale parameters, porosity distribution, functionally graded pattern, elastic foundations and geometrical parameters on the thermoelastic response of tubes. The obtained results highlight the importance of static/dynamic analysis of FG porous nanotubes in the thermal pre-buckling and post-buckling regimes.