Abstract

This paper investigates the dynamic characteristics of rotating functionally graded material (FGM) micro-beams based on Euler–Bernoulli beam theory, Euler–Bernoulli beam theory incorporating shear deformation, and Timoshenko theory. The deformation field of the micro-beam is described within a floating coordinate system using the meshless point interpolation method (PIM/RPIM). The couple stress tensor and curvature tensor, which capture the size effect, are incorporated into the potential energy formulation. Employing Lagrange’s equations of the second kind, a higher-order rigid-flexible coupled dynamic model for rotating FGM micro-beams is established under various beam theories. Simulation results obtained from the Euler–Bernoulli theory with shear correction and the Timoshenko model are compared with those from the classical beam model and previous literature. The influences of material gradient index, material characteristic length parameter, and rotational speed profiles on the transient dynamic response and steady-state free vibration of rotating micro-beams are systematically examined. The results show that increasing the material gradient index reduces the structural stiffness, resulting in lower natural frequencies and larger vibration amplitudes, whereas increasing the characteristic length parameter enhances the size effect and improves system stiffness.

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