Nonlinear forced vibration of strain gradient microbeams |
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Authors: | R. Vatankhah M.H. Kahrobaiyan A. Alasty M.T. Ahmadian |
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Affiliation: | 1. School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran;2. Center of Excellence in Design, Robotics and Automation (CEDRA), Sharif University of Technology, Tehran, Iran |
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Abstract: | In this paper, the strain gradient theory, a non-classical continuum theory able to capture the size effect happening in micro-scale structures, is employed in order to investigate the size-dependent nonlinear forced vibration of Euler–Bernoulli microbeams. The nonlinearities are caused by mid-plane stretching and nonlinear external forces such as van-der-Waals force. The nonlinear governing equations of the microbeams are solved analytically utilizing the perturbation techniques. The primary, super-harmonic and sub-harmonic resonances of a microbeam are studied and the size-dependency of the frequency responses is assessed. The results indicate that the nonlinear forced vibration behavior of microbeams is size-dependent and the ratio of the microbeam thickness to the material length scale parameter, an additional material property appearing in the strain gradient theory, plays an important role. |
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Keywords: | Strain gradient theory Microbeam Size-dependency Length scale parameter Nonlinear vibration |
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