Free vibration of nanorings/arches based on nonlocal elasticity

This paper deals with the free vibration problem of nanorings/arches. The problem is formulated on the basis of Eringen’s nonlocal theory of elasticity in order to allow for the small length scale effect. Exact vibration frequencies are derived for the nanorings/arches and the effects of small length scale, defects, and elastic boundary conditions are investigated. The small length scale effect lowers the vibration frequencies. The defects and the use of elastic boundary conditions (instead of fixed restraints) also significantly reduce the frequencies and alter the vibration mode shapes of circular rings/arches. The results presented should be useful to engineers who are designing nanorings/arches for microelectromechanical and nanoelectromechanical devices.

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