Abstract
In this paper, a differential quadrature element method (DQEM) is proposed for free vibration analysis of rotating non-uniform nanocantilevers carrying multiple concentrated masses. Employing Hamilton’s principle, the governing equations of rotating nanoblades, modeled by the nonlocal Timoshenko beam theory, are derived. The differential quadrature (DQ) analogs of the governing equations of motion, compatibility conditions at the positions of masses, and related boundary conditions are established, and then, an eigen-value problem is obtained. The vibration characteristics of the problem are investigated with various conditions of number, positions, and magnitudes of the masses, while the cross section, rotational velocity, hub radius, and nonlocal parameters are arbitrary. The accuracy of the results is confirmed by the exact data available in the literature. In comparison with the other applicable methods, DQEM is less time-consuming and also enables the researcher to analyze the problem under arbitrary conditions, which are complex or even sometimes impossible to solve. The studies show that rotation rates, geometric properties, and masses conditions can contribute significantly in the dynamic characteristics of rotating N/MEMS devices such as nanoturbines, nanoscale molecular bearings, shaft and gear, and nanosensors.
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