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

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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 Sanders–Koiter’s shell theory and considering the small size effects by employing Eringen’s 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 atomistic–continuum 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.

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Acknowledgements

This research was carried out in the framework of project N\({^{\circ }}\) 030348, POCI-01-0145-FEDER-030348, “Laminated composite panels reinforced with carbon nanotubes and curvilinear carbon fibres for enhanced vibration and flutter characteristics”, funded by FEDER, through Programa Operacional Competitividade e Internacionalização – COMPETE 2020, and by National Funds (PIDDAC), through FCT/MCTES.

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  1. DEMec/INEGI, Faculdade de Engenharia, Universidade do Porto, R. Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal

    Eduardo Henrique Gonçalves & Pedro Ribeiro

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Correspondence to Pedro Ribeiro.

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Gonçalves, E.H., Ribeiro, P. Modes of Vibration of Single- and Double-Walled CNTs with an Attached Mass by a Non-local Shell Model. J. Vib. Eng. Technol. 10, 375–393 (2022). https://doi.org/10.1007/s42417-021-00381-z

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