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Nonlinear forced vibration of strain gradient microbeams. (English) Zbl 1426.74194
Summary: 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.

MSC:
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H45 Vibrations in dynamical problems in solid mechanics
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