Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration analysis

This paper aims to study vibration characteristics of chiral and zigzag double-walled carbon nanotubes entrenched on Donnell shell model. The Eringen\'s nonlocal elastic equations are being combined with Donnell shell theory to observe small scale response. Wave propagation is proposed technique to establish field equations of model subjected to four distinct end supports. A nonlocal model has been formulated to explore the frequency spectrum of both chiral and zigzag double-walled CNTs along with diversity of indices and nonlocal parameter. The significance of scale effect in relevance of length-to-diameter and thickness- to- radius ratios are discussed and displayed in detail. The numerical solution based on this nonlocal Donnell shell model can be further used to predict other frequency phenomena of double-walled and multi-walled CNTs.