Nonlinear Effects on Resonance Behaviour of Beams in Micro Scale
Nonlinear free and forced oscillation of microscale simply supported beams is investigated in this paper. Introducing a material length scale parameter, the nonlinear model is conducted within the context of non-classical continuum mechanics. By using a combination of the modified couple stress theory and Hamilton’s principle the nonlinear equation of motion is derived. The nonlinear frequencies of a beam with initial lateral displacement are discussed. Equations have been solved using an exact method for free vibration and multiple times scales (MTS) method for forced vibration and some analytical relations have been obtained for natural frequency of oscillations. The results have been compared with previous work and good agreement has been obtained. Also forced vibrations of system in primary resonance have been studied and the effects of different parameters on the frequency-response have been investigated. It is shown that the size effect is significant when the ratio of characteristic thickness to internal material length scale parameter is approximately equal to one, but is diminishing with the increase of the ratio. Our results also indicate that the nonlinearity has a great effect on the vibration behavior of microscale beams.
H. Nourbakhsh et al., "Nonlinear Effects on Resonance Behaviour of Beams in Micro Scale", Applied Mechanics and Materials, Vols. 110-116, pp. 4178-4186, 2012