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Acta Mechanica Solida Sinica

, Volume 26, Issue 1, pp 21–34 | Cite as

A Nonlinear Microbeam Model Based on Strain Gradient Elasticity Theory

  • Farshid Rajabi
  • Shojaa Ramezani
Article

Abstract

A micro scale nonlinear beam model based on strain gradient elasticity is developed. Governing equations of motion and boundary conditions are obtained in a variational framework. As an example, the nonlinear vibration of microbeams is analyzed. In a beam having a thickness to length parameter ratio close to unity, the strain gradient effect on increasing the natural frequency is predominant. By increasing the beam thickness, this effect decreases and geometric nonlinearity plays the main role on increasing the natural frequency. For some specific ratios, both geometric nonlinearity and size effects have a significant role on increasing the natural frequency.

Key words

strain gradient elasticity microbeam geometric nonlinearity 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIslamic Azad UniversityAnzaliIran
  2. 2.Department of Mechanical Engineering, Faculty of EngineeringUniversity of GuilanRashtIran

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