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Numerical Simulation of Modal Vibration Response of Wavy Carbon Nanotubes

Department of Mechanical Engineering Wayne State University, Detroit, MI 48201, USA

Ronald F. Gibson

Department of Mechanical Engineering Wayne State University, Detroit, MI 48201, USA, ronaldgibson{at}unr.edu

The potential use of carbon nanotubes (CNTs) in applications such as reinforcing materials in nanocomposites has motivated interest in the measurement of their mechanical properties. Several researchers have used the experimentally measured resonance frequencies of CNTs, along with classical beam theory for straight beams to `back out' CNT modulus values. However, from photomicrographic images of CNTs, it is clear that they are not straight, and that they typically have significant waviness or curvature associated with them. This research involves the development of carbon nanotube models using the finite element (FE) approach and the benchmarking of the developed models against results from other models and experiments. Subsequently, the FE models were used to study the effect of waviness and aspect ratio on the modal vibration response of CNTs, so that a better understanding of the characterization of their mechanical properties can be established. It was found that significant errors in `backed out' modulus values of CNTs can occur when waviness is not accounted for in modal analysis. For example, with a change in waviness factor (amplitude of waviness divided by the projected length of the CNT) from 0 to 0.6, frequency values can change by 29% for the fundamental mode, and the corresponding change in the `backed out' modulus from the straight beam equation can be as high as 66%. The analysis of vibrating CNTs is also important in studies of the sonication process for improving dispersion of CNTs in manufacturing of nanocomposites.

Key Words: single-walled carbon nanotube • waviness • fundamental mode.

This version was published on March 1, 2009

Journal of Composite Materials, Vol. 43, No. 5, 501-515 (2009)
DOI: 10.1177/0021998308097676


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