On the torsional vibration of nanorods surrounded by elastic matrix via nonlocal FEM

Nonlocal dynamic torsional response of nanorods embedded in elastic media is investigated. It is considered that mechanical behavior of elastic media is supposed to be like linear foundation model. The nonlocal dynamic torsion equation is obtained according to Hamilton's Principle. Application of solved motion of equation is performed for nanorod models that have torsional spring attachment at the one end as well as three different general boundary conditions. Moreover, the formulation of nonlocal finite element method (NL-FEM) based on weighted residual that considers stiffness of elastic media and attachment ratio is attained; this finite element formula is new in the literature. The nondimensional torsional frequencies are presented under nanorod length, nondimensional nonlocal parameter, slenderness ratio, nondimensional media stiffness parameter and stiffness ratio of attachment as tables and graphics comparatively with NL-FEM. This study is exhibited that NL-FEM can be used for torsional vibration analysis of nanorods embedded in elastic media.