LAUSR

This study aims to consider the nonlocal effect on internal resonances of nanorods in nonlinear axial vibration. To this end, the nonlocal nonlinear governing equation of motion and boundary conditions are derived by implementing Hamilton’s principle. A new method is also introduced for converting local equations to nonlocal ones. The multi-mode Galerkin method over the space variable is used to convert the partial differential equation to the ordinary differential type. Due to the nonlinearity terms arisen in the equation, a perturbation problem was considered, and a multiple-scale analysis was employed. The cases for exciting the internal resonances were introduced, and the effects of various parameters like the nanorod length, motion amplitude, and nonlocal parameter on natural frequencies were investigated. The determined correlation of the internal resonances of the nanorod with the parameters is key in safe designing the structure in as much as additional mode shapes are excited, and a greater energy is generated. It is believed that the current study comprehensively investigates the behavior of nanorods utilized in nanoelectromechanical systems.