Free vibration analysis of a rotating nanobeam using integral form of Eringen’s nonlocal theory and element-free Galerkin method

To uncover the inconsistencies among different kernel functions, two special cases of Eringen’s nonlocal theory, including the TPNI model and a modified model proposed by Eptaimeros are employed in the current investigation. Current research makes use of the integral form of Eringen’s nonlocal theory instead of the popular differential one to avoid the potential paradoxes. The Timoshenko beam theory is adopted to model rotating nanobeams with and without nonzero setting angles. Considering the number of existing applications of the element-free Galerkin method on nonlocal nanoscale beams are few, the element-free Galerkin method has been employed to develop numerical solutions. Free vibration frequencies of rotating nanobeams and local beams for varying rotating angular velocities have been studied. During the analyses of rotating effects, the factor of size effect is discussed. Size effects of rotating nanobeams for varying rotating angular velocities are examined. The impact on size effects contributed by rotating effects is evaluated. By comparing the vibration frequencies of two nonlocal models, inconsistencies between different kernel functions are uncovered.