TORSIONAL WAVE PROPAGATION AND VIBRATION OF CIRCULAR NANOSTRUCTURES BASED ON NONLOCAL ELASTICITY THEORY

The presence of size effects represented by a small nanoscale on torsional wave propagation properties of circular nanostructure, such as nanoshafts, nanorods and nanotubes, is investigated. Based on the nonlocal elasticity theory, the dynamic equation of motion for the structure is formulated. By using the derived equation, simple analytical solutions for the relation between wavenumber and frequency via the differential nonlocal constitutive relation and the numerical solutions for a discrete nonlocal model via the integral nonlocal constitutive relation have been obtained. This results not only show that the dispersion characteristics of circular nanostructures are greatly affected by the small nanoscale and the classical theory overestimates the stiffness of nanostructures, but also highlights the significance of the integral nonlocal model which is able to capture some boundary characteristics that do not appear in the differential nonlocal model.