Free vibration analysis of rotating nano-beams for flap-wise, chord-wise and axial modes based on Eringen's nonlocal theory

Abstract

A mathematical model based on Eringen's nonlocal elasticity theory is presented to analyze free vibration behavior of rotating nano-beams. The model is capable of studying the flap-wise and chord-wise vibrations as well as the axial vibration of rotating nano-beams. The model is based on Euler-Bernoulli beam theory, and incorporates spin-softening and Coriolis effects. Hamilton's principle is employed to derived the governing equations involving virtual displacements, and Ritz method is followed to discretize the governing equations. The governing equations are transformed to an eigenvalue problem in state-space. The stable solutions in frequency domain are indentified by appropriately examining the nature of the complex eigenvalues. The model is validated through some reduced problems available in the literature. The non-dimensional speed-frequency behaviors are presented and discussed for different normalized nonlocal parameters, hub parameters and section aspect ratios. The spin-softening and Coriolis effects are individually illustrated and discussed. The present advanced model for rotating nano-beams is reported for the first time. The present study would help in understanding the dynamics of rotating nano-beams in a comprehensive manner.