Manifestation of Strain Gradients in Nanostructural Vibration

Our paper is concerned with the manifestation of strain gradients (SG) in the vibration of nanostructures such as zinc oxide nanowires, polymeric nanofibers, carbon nanotubes, etc. The motivation for our research is based on the need to explain the well-documented size-dependent behavior in the elastic modulus of nanostructures. It has been experimentally observed in a nanostructure that as one of its lateral dimensions decreases past a characteristic value, its elastic modulus begins to exhibit an exponential rise, often, to the order of several hundred percent or more! In our work, we employ the SG theory to formulate a rational and physics-based approach to account for the size-dependent phenomenon in nanostructures. We showed that the 3 SG length-scale parameters for centrosymmetric and isotropic materials can be combined into a single effective parameter to facilitate its experimental determination in bending vibration. Further, it would be of interest to understand how the natural frequencies and mode shapes of nanostructures are modified by the manifestation of SG. Several examples are provided to demonstrate such dependencies. Our SG-based vibrational model therefore, represents an attempt to capture the highly inverse size-dependent effects in the mechanics of nano-scale materials for both their static and dynamic responses.