Investigation of the small-scale effects on the three-dimensional flexural vibration characteristics of a basic model for micro-engines

The coupled three-dimensional flexural vibrations of a micro-rotating shaft-disk system, as a basic model for micro-engines, are investigated in this paper by considering small-scale effects utilizing the modified couple stress theory. Governing equations of motion are derived by the use of Hamilton's principle. Then, implementing the Galerkin approach, an infinite set of ordinary differential equations is obtained for the system. With truncated two-term equations, expressions for the first two natural frequencies are written, and for the two corresponding modes, the maximum rotational speed up to which the system will be stable is analytically determined. Parametric studies on the results for different responses illustrate that the length-scale value has a significant effect on the natural frequencies of the shaft and the threshold of instability of the system.