Modes of Vibration of Single- and Double-Walled CNTs with an Attached Mass by a Non-local Shell Model

Abstract

Purpose: It is intended to investigate the modes of vibration of single-walled and double-walled carbon nanotubes with an attached mass, to gain knowledge useful for the application of CNTs for mass and cell detection. A related goal is the development and validation of a shell model that can be applied for the former purpose. Methods: A p-version finite element method model based on SandersKoiters shell theory and considering the small size effects by employing Eringens non-local theory is employed. Van der Waals forces are included in the interlayer stiffness of DWCNTs. Concentrated attached masses are included through their inertia, which is affected by non-local terms. The convergence and validity of the models are tested by comparisons to Molecular Dynamics simulations and atomisticcontinuum hybrid finite element analysis. Results: Studies are conducted on the influence of the non-local parameter, which is calibrated for natural frequencies of different order and CNTs of different lengths. Critical values of length for which the non-local theory remains relevant depend upon the equivalent material and geometric properties employed, but more important is the verification that the non-local shell theory can be used to improve the accuracy of continuum CNT models. The dynamic behaviour of bridged SWCNTs and DWCNTs is studied, examining their applicability in mass detection devices. Conclusion: The large influence a localised mass has on the mode shapes of vibration is illustrated. Sensitivity increases more significantly in lower length carbon nanotubes. Furthermore, it is found that SWCNTs have a higher sensitivity to attached concentrated masses than DWCNTs with similar diameter, making the former more appealing candidates for mass detection nanodevices. (c) 2021, Krishtel eMaging Solutions Private Limited.