Continuum Mechanics and Thermodynamics

, Volume 27, Issue 4–5, pp 583–607 | Cite as

On free oscillations of an elastic solids with ordered arrays of nano-sized objects

  • Victor A. EremeyevEmail author
  • Elena A. Ivanova
  • Nikita F. Morozov
Original Article


We discuss free oscillations of some elastic structures consisting of an elastic substrate and an ordered array of aligned nano-sized objects. Considering various shapes of nano-objects such as beams, tubes, and spheres, we investigate the spectrum of eigenfrequencies of these structures in comparison with the spectra of one nano-object and of the substrate. As a result, we find the correspondence between the spectrum of whole structure and the spectrum of one nano-object, which gives the possibility to determine few first eigenfrequencies of nano-sized objects.


Free oscillations Ordered array Nanomechanics Nanorod Nanoplate Nanosphere Eigenfrequencies analysis 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Victor A. Eremeyev
    • 1
    • 2
    Email author
  • Elena A. Ivanova
    • 3
    • 4
  • Nikita F. Morozov
    • 4
    • 5
  1. 1.Faculty of Mechanical EngineeringOtto-von-Guericke-UniversityMagdeburgGermany
  2. 2.South Scientific Center of RASci and South Federal UniversityRostov on DonRussia
  3. 3.St. Petersburg State Polytechnical UniversitySt. PetersburgRussia
  4. 4.Institute of Problems of Mechanical Engineering of RASciSt. PetersburgRussia
  5. 5.St. Petersburg State UniversitySt. PetersburgRussia

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