free axial and torsional vibration of boron nitride nanorods using nonlocal finite element method

In this study, the formulation of nonlocal finite elements is developed for nanorods under axial and torsional vibrations using nonlocal elasticity theory. first, an overview of the topic is provided along with review of relevant studies in literature. next, the fundamental formulations of nonlocal elasticity theory are presented, and the corresponding equations of motion for axial and torsional vibrations are derived. based on these formulations, the stiffness and polar inertia matrices of the nanorod are obtained using the weighted residual method. finally, the numerical results are illustrated through graphical representations, highlighting the effects of nanorod length, the number of finite elements, and the nonlocal parameters.