Thermal stress effects on size-dependent nonlinear axial vibrations of nanorods exposed to magnetic fields surrounded by nonlinear elastic medium

Abstract

Taking von Kármán geometric nonlinearity into account, this research proposes a nonlinear model of nanorod, based on the nonlocal elasticity and axial beam theories. Imperfect nanorod is surrounded by nonlinear elastic medium and is subjected to the axial compression or various fields in terms of thermal and transvers magnetic loads. Pinned–pinned boundary conditions are immovable and free for the nanorod under axial compression considering thermal and magnetic loads. The governing equilibrium equations of the nanorod are derived by means of Hamilton's principle. The coupled nonlinear dimensionless differential equations are solved employing He's variational method. To evaluate the accuracy of the results, the results of this method are compared with the values obtained from the finite element method. Numerical results are provided to explore the influences of the low and high temperatures, nonlocal parameter, magnetic force of transverse field, amplitude of vibrations, and linear and nonlinear elastic materials for nanorods.