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Establishing detection maps for carbon nanotube mass sensors: molecular versus continuum mechanics

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Abstract

In this work, the mass-sensing ability and the corresponding detection efficiency of a fully clamped single-walled carbon nanotube (SWCNT) are investigated through a free vibration analysis, by utilizing mainly a molecular mechanics (MM) formulation and secondarily a continuum mechanics (CM) analytical approximation. The MM method is based on representing the SWCNT as a three-dimensional (3D) finite element frame of point masses and linear springs, while the CM one is grounded on the Euler–Bernoulli beam theory. The overall effort is focused on obtaining detection maps, based on natural frequency data which are capable of leading to the straightforward identification of an unknown mass attached to the external surface of the candidate SWCNT sensor. For this reason, the SWCNT relative natural frequency shifts due to the mass addition, regarding specific modes of vibration and for a variety of mass magnitude and position combinations, are calculated beforehand. Then, the magnitude as well as the position of the added mass may be graphically found by superposing the arisen relative natural frequency shift variations in common contour diagrams. Some results from the open literature are utilized to confirm the predictive performance of the proposed MM method concerning the free vibration of pure SWCNTs, while the MM and CM established detection maps are set in contrast to examine whether a mass nanosensor may be satisfactorily treated in a continuum manner.

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Authors and Affiliations

  1. Materials Science Laboratory, Department of Mechanical Engineering, Technological Educational Institute of Western Greece, 1 Megalou Alexandrou Street, 26334, Patras, Greece

    Georgios I. Giannopoulos

  2. Department of Materials Science, University of Patras, 26504, Patras, Greece

    Georgios I. Giannopoulos

  3. Machine Design Laboratory, Department of Mechanical Engineering and Aeronautics, University of Patras, Rio, 26500, Patras, Greece

    Stylianos K. Georgantzinos

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  1. Georgios I. Giannopoulos
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Correspondence to Georgios I. Giannopoulos.

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Giannopoulos, G.I., Georgantzinos, S.K. Establishing detection maps for carbon nanotube mass sensors: molecular versus continuum mechanics. Acta Mech 228, 2377–2390 (2017). https://doi.org/10.1007/s00707-017-1812-9

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  • DOI: https://doi.org/10.1007/s00707-017-1812-9

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