Keywords: double-walled carbon nanotube, continuum's vibrations, time domain identification, bacterium mass sensor, continuous system, sensitivity analysis.

Since the revolutionary work by Ijima [1] the field of nanotechnology has attracted many researchers. In this field carbon nanotubes have demonstrated a significant potential for use in a diverse range of new and evolving applications. Many studies have been also performed for investigating their mechanical behaviour, vibrations and buckling phenomena [2].

The vibrations and identification of the cantilever double walled carbon nanotube with an attached bacterium or virus, by adopting a time domain parametric identification technique [3], are studied in this paper. The basic idea of the method consists of the minimization of the so called penalty function representing the squared difference between selected measured response parameters and the correspondent quantities determined through the study of a pertinent finite element model. In Cacciola et al. [4], by means the definition of a suitable penalty function, the standard bounded variables least square approach has been used as the method vehicle for identifying selected structural parameters of both the time-domain deterministic and stochastic response. In this context a computationally competitive procedure for determining the pertinent sensitivity matrix has been proposed [5].

The proposed procedure, according to the philosophy of the above described identification method requires the following steps: (i) the adoption of the mechanical beam model in order to write the differential equations governing the problem; (ii) the application of the weighted residuals method to discretize the problem; (iii) the minimization of a penalty function chosen as the difference between measured and estimated time-histories of selected dynamic response parameters; and (iv) the determination of the response sensitivities.

In this paper the aim is to identify two unknown parameters, namely the attached mass and its position, by using measured displacement time histories of a fixed-free double-walled carbon nanotube.

1

S. Iijima, "Helical microtubes of Graphite Carbon", Nature, 354, 56-58, 1991. doi:10.1038/354056a0

2

I. Elishakoff, D. Pentaras, "Some modern problems in structural engineering dynamics", Shock and Vibration, 2010. doi:10.3233/SAV-2010-0530

3

H. Imai, C. B. Yun, O. Maruyama, M. Shinozuka, "Fundamentals of system identification in structural dynamics", Probabilistic Engineering Mechanics, 4, 162-173, 1989. doi:10.1016/0266-8920(89)90022-2

4

P. Cacciola, N. Maugeri, G. Muscolino, "A Method for the Deterministic and Stochastic Time Domain Identification of Structures", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 155, 2008. doi:10.4203/ccp.88.155

5

P. Cacciola, P. Colajanni, G. Muscolino, "A modal approach for the evaluation of the response sensitivity of structural systems subjected to non-stationary random process", Computer Methods in Applied Mechanics and Engineering, 194, 4344-4361, 2005. doi:10.1016/j.cma.2004.11.006

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