A nonlinear microbeam model based on strain gradient elasticity theory with surface energy |
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Authors: | Farshid Rajabi Shojaa Ramezani |
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Institution: | (1) Department of Mechanics, Huazhong University of Science and Technology, Wuhan, 430074, China;(2) Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan, 430074, China; |
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Abstract: | A microscale nonlinear Bernoulli–Euler beam model on the basis of strain gradient elasticity with surface energy is presented.
The von Karman strain tensor is used to capture the effect of geometric nonlinearity. Governing equations of motion and boundary
conditions are obtained using Hamilton’s principle. In particular, the developed beam model is applicable for the nonlinear
vibration analysis of microbeams. By employing a global Galerkin procedure, the ordinary differential equation corresponding
to the first mode of nonlinear vibration for a simply supported microbeam is obtained. Numerical investigations show that
in a microbeam having a thickness comparable with its material length scale parameter, the strain gradient effect on increasing
the beam natural frequency is higher than that of the geometric nonlinearity. By increasing the beam thickness, the strain
gradient effect decreases or even diminishes. In this case, geometric nonlinearity plays the main role on increasing the natural
frequency of vibration. In addition, it is shown that for beams with some specific thickness-to-length parameter ratios, both
geometric nonlinearity and size effect have significant role on increasing the frequency of nonlinear vibration. |
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