In-plane free vibration analysis of nonlocal nanorings embedded in elastic medium

Atomic scaled rings are included as mechanical components in nano-electro-mechanical systems (NEMS). It is known from experimental results that the classical elasticity solution is insufficient in the mechanical analysis of such components. This problem is eliminated with the nonlocal elasticity solution. In this study, it is aimed to investigate the size-dependent dynamics of nano scaled rings embedded in linear elastic medium for the first time in the scientific literature. First, the nonlocal in-plane free vibration of nanorings is formulated. Then the free vibration frequency equation is obtained. The nondimensional frequencies of different modes of nanorings are presented according to different parameters and the numerical results are discussed in detail. According to the results, while nonlocal parameter reduces the nondimensional frequencies, nanoring radius increases the nondimensional parameters. Additionally, frequencies of nanorings are increased by elastic medium. The results show that the atomic size effect and elastic environment are important on the mechanical behavior of nanorings.