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. © 2013 Elsevier Inc.
Vatankhah, R., Kahrobaiyan, M. H., Alasty, A., & Ahmadian, M. T. (2013). Nonlinear forced vibration of strain gradient microbeams. Applied Mathematical Modelling, 37(18–19), 8363–8382. https://doi.org/10.1016/j.apm.2013.03.046