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A nonlinear Timoshenko beam formulation based on the modified couple stress theory

Asghari, M ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ijengsci.2010.09.025
  3. Abstract:
  4. This paper presents a nonlinear size-dependent Timoshenko beam model based on the modified couple stress theory, a non-classical continuum theory capable of capturing the size effects. The nonlinear behavior of the new model is due to the present of induced mid-plane stretching, a prevalent phenomenon in beams with two immovable supports. The Hamilton principle is employed to determine the governing partial differential equations as well as the boundary conditions. A hinged-hinged beam is chosen as an example to delineate the nonlinear size-dependent static and free-vibration behaviors of the derived formulation. The solution for the static bending is obtained numerically. The solution for the free-vibration is presented analytically utilizing the method of multiple scales, one of the perturbation techniques
  5. Keywords:
  6. Non-classic continuum theories ; Timoshenko beam ; Classical continuum theory ; Continuum theory ; Couple stress ; Couple stress theory ; Free vibration ; Free vibration behavior ; Hamilton principle ; Method of multiple scale ; New model ; Nonlinear behavior ; Size effects ; Static bending ; Timoshenko beam model ; Timoshenko beams ; Boundary conditions ; Continuum mechanics ; Nonlinear analysis ; Particle beams ; Vibration analysis ; Perturbation techniques
  7. Source: International Journal of Engineering Science ; Volume 48, Issue 12 , 2010 , Pages 1749-1761 ; 00207225 (ISSN)
  8. URL: http://www.sciencedirect.com/science/article/pii/S0020722510002107