On the Eigenfrequencies of an Ordered System of Nanoobjects

  • Victor A. Eremeyev
  • Holm Altenbach
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 13)


A method is discussed to determine the eigenfrequencies of nanostructures (nanotubes, nanospheres, and nanocrystals) by measuring the eigenfrequencies of a ‘large system’ that consists of an array of vertically oriented similar nanotubes or nanocrystals equidistantly grown on a substrate. It is shown that the eigenfrequen-cies of a single nanoobject can be derived from the eigenfrequency spectra of the large (array-substrate) system and of the substrate. With other words, using experimental data for large systems one can determine the eigenfrequencies of a single nanoobject. The method can be also applied to systems of nanotubes grown in parallel to the substrate and to the systems of micro- and nanospheres. The modeling of nanocomposite plates using the direct approach to the shell theory is discussed. The effective stiffness tensors are considered. As an example, the eigenfrequencies of an array of ZnO micro- or nanocrystals and GaAs multiwalled nanotubes on a sapphire substrate are calculated.


Large System Sapphire Substrate Natural Vibration Shell Theory Effective Stiffness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, B.V. 2009

Authors and Affiliations

  • Victor A. Eremeyev
    • 1
  • Holm Altenbach
    • 2
  1. 1.South Scientific CenterRASci South Federal UniversityRostov on DonRussia
  2. 2.Lehrstuhl für Technische Mechanik, Zentrum für IngenieurwissenschaftenMartin-Luther-Universität Halle-WittenbergHalle (Saale)Germany

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