On the eigenfrequencies of an ordered system of nanoobjects

Amethod 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 eigenfrequencies 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. © Springer Science+Business Media B.V. 2009.