Journal
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
Volume 48, Issue 12, Pages 1749-1761Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijengsci.2010.09.025
Keywords
Non-classic continuum theories; Couple stress; Timoshenko beam; Nonlinear analysis
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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. (C) 2010 Elsevier Ltd. All rights reserved.
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