Vibration analysis of curved graphene ribbons based on an elastic shell model

• Orthotropic elastic shell model is proposed for predicting vibration characteristics of curved graphene ribbons.
• The effect of a small length scale is incorporated by using the gradient elasticity theory.
• The influences of some physical parameters are investigated.

An orthotropic elastic shell model is developed to study the vibration characteristics of curved graphene ribbons (CGRs). The effect of a small length scale is incorporated in the formulations using the gradient elasticity theory. Novozhilov's linear shallow shell theory is used and it is assumed that CGR is simply supported. Analytical solution to the equations is proposed to obtain the frequencies of CGRs. The vibrational properties of CGRs are investigated with respect to the variations of various parameters. Results indicate significant dependence of natural frequencies on the curvature change as well as the modes being considered.