Scale-dependent torsional vibration response of non-circular nanoscale auxetic rods

Abstract

In the current paper, analysis of torsional vibration behavior of non-circular nanorods made of auxetic honeycomb material is investigated for the first time. The triangular and elliptical cross-sections are selected to be analyzed. Moreover, one of the distinct properties of auxetic honeycomb materials is that they possess a negative Poisson’s ratio, which can be effective on the design and analysis of structures. In order to capture a small size or scale effect, the constitutive relation of nanorods is modified based on Eringen’s nonlocal elasticity theory (ENET). Hamilton’s principle is employed to obtain the kinematic relation of nanoscale rods. The nonlocal derived governing equations of non-circular auxetic nanorods are solved by utilizing an analytical method with respect to different boundary conditions. In order to verify the correctness of obtained outcomes, the results are compared to previous investigations, and good agreement can be observable. The influences of various parameters such as both Clamped–Clamped (C–C) and Clamped-Free (C-F) boundary conditions, nonlocal parameters, inclined angles, and geometrical ratios are explored and illustrated in the framework of several figures, which can be seen in detail.