On the stability of a microbeam conveying fluid considering modified couple stress theory

In this paper, the size-dependent vibrational behavior of a microbeam conveying fluid was investigated using the Modified Couple Stress Theory. For cantilever and clamped-clamped microbeams, the small amplitude vibration equation of the microbeams was solved using a Galerkin based reduced order model and the effects of material length-scale parameter on its natural frequencies were evaluated. It was found that for the both cantilever and clamped-clamped conditions, the critical fluid velocities predicted by the modified couple stress theory are higher than those predicted by the classical beam theory. In addition, the differences between the eigen-frequencies and the critical fluid velocities predicted by the modified couple stress theory and classical beam theory depends on the ratio of the material length-scale parameter to the beam height. In addition an unexpected result in the difference between the first eigen-frequency of the cantilever micro-beam obtained by the classical and the modified couple stress theory has been achieved.