Nonlinear size-dependent forced vibrational behavior of microbeams based on a non-classical continuum theory

In this paper, the nonlinear forced-vibration of Euler-Bernoulli beams with large deflections is investigated based on the modified couple stress theory, a non-classical theory capable of capturing size effects. The classical theory is unable to predict the size effects. In systems with the dimensions in order of microns and sub-microns the size effects are very significant. For some specific beams subjected to a concentrated force at its middle as the harmonic exciter, the size-dependent responses are investigated for primary, super-harmonic and sub-harmonic resonances. The results show that the frequency-responses of the system are highly size-dependent.