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Applied Mathematics and Mechanics

, Volume 37, Issue 5, pp 583–600 | Cite as

Nonlinear beam formulation incorporating surface energy and size effect: application in nano-bridges

  • A. Koochi
  • H. Hosseini-ToudeshkyEmail author
  • M. Abadyan
Article

Abstract

A nonlinear beam formulation is presented based on the Gurtin-Murdoch surface elasticity and the modified couple stress theory. The developed model theoretically takes into account coupled effects of the energy of surface layer and microstructures sizedependency. The mid-plane stretching of a beam is incorporated using von-Karman nonlinear strains. Hamilton’s principle is used to determine the nonlinear governing equation of motion and the corresponding boundary conditions. As a case study, pull-in instability of an electromechanical nano-bridge structure is studied using the proposed formulation. The nonlinear governing equation is solved by the analytical reduced order method (ROM) as well as the numerical solution. Effects of various parameters including surface layer, size dependency, dispersion forces, and structural damping on the pullin parameters of the nano-bridges are discussed. Comparison of the results with the literature reveals capability of the present model in demonstrating the impact of nanoscale phenomena on the pull-in threshold of the nano-bridges.

Key words

surface energy size effect nonlinear beam formulation electromechanical nano-bridge pull-in instability 

Chinese Library Classification

O343.5 

2010 Mathematics Subject Classification

74A60 74N15 81T55 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringAmirkabir University of TechnologyTehranIran
  2. 2.Mechanical Engineering Group, Shahrekord BranchIslamic Azad UniversityShahrekordIran

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