Microsystem Technologies

, Volume 24, Issue 8, pp 3521–3536 | Cite as

Axial magnetic field effects on dynamic characteristics of embedded multiphase nanocrystalline nanobeams

  • Farzad EbrahimiEmail author
  • Mohammad Reza Barati
Technical Paper


This article investigates vibrational behavior of a multi-phase nanocrystalline nanobeam resting on Winkler–Pasternak foundation and subjected to a longitudinal magnetic field in the framework of nonlocal couple stress and surface elasticity theories. In this model, the essential measures to describe the real material structure of nanocrystalline nanobeams and the size effects were incorporated. This non-classical nanobeam model contains couple stress effect to capture grains micro-rotations. Moreover, the nonlocal elasticity theory is employed to study the nonlocal and long-range interactions between the particles. The present model can degenerate into the classical model if the nonlocal parameter, couple stress and surface effects are omitted. Hamilton’s principle is employed to derive the governing equations and the related boundary conditions which are solved applying differential transform method. The frequencies are compared with those of nonlocal and couple stress based beams. It is showed that vibration frequencies of a nanocrystalline nanobeam depend on the grain size, grain rotations, porosities, interface, elastic foundation, magnetic field, surface effect, nonlocality and boundary conditions.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Faculty of EngineeringImam Khomeini International UniversityQazvinIran

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