Torsional vibration analysis of scale-dependent non-circular graphene oxide powder-strengthened nanocomposite nanorods

This paper studies on size-dependent torsional dynamic response of non-circular graphene oxide powders (GOPs)-strengthened nanocomposite nanorods for the first time. The elliptical and triangular cross sections are chosen to be explored. Additionally, GOPs are distributed uniformly into polymeric matrix. In this paper, both Halpin-Tsai homogenization method and rule of mixture are implemented to estimate effective mechanical properties of nanocomposite structure. To take into account influence of small size, the constitutive relations of nanorods are developed on the basis of Eringen's nonlocal elasticity theory (ENET). The principle of virtual work is applied to obtain the kinetic and kinematic relations of nanoscale rods. The nonlocal derived governing equations of non-circular GOPs-reinforced nanocomposite nanorods are solved by utilizing an analytical method with respect to different boundary conditions. To verify the accuracy of obtained outcomes, the results are compared to previous investigations and suitable agreement can be observable. The influences of various parameters such as both Clamped-Free (C-F) and Clamped-Clamped (C-C) boundary conditions, nonlocal parameter, inclined angles and geometrical ratio are explored and illustrated in the framework of several figures which can be observed in detail.