Vibration analysis of Bi-directional FG-GNPs reinforced rotating micro-beam under Thermo-mechanical loading

Abstract

Functionally graded metal matrix and graphene nano-platelets (GNPs) reinforced composites have wide usage in present days. Such materials have high strength-to-weight ratios, good energy efficiency and absorption ability, high thermal conductivity. Due to these properties, they are used widely in micro-electromechanical systems, aerospace, automotive, and biomedical applications. Further, micro-beams are used in micro-sensors, micro turbines and rotors, which are subjected to severe fatigue loads. Adding nano-fillers as reinforcement to metal foams improves the stiffness to weight ratio. Present work deals with vibration analysis of functionally graded GNPs reinforced metallic core rotating micro-beam of taper section. The micro-beam is exposed to thermal environment under centrifugal loads due to rotation. Material modelling and dynamic formulation of the beam are first derived using Halpin-Tsai model and variational approach using modified couple stress theory. The material length scale parameter (MLSP) and functionally grading parameters in thickness and length directions are considered. The solutions are obtained using Ritz approximation technique. A validation study is performed to check the accuracy of present model. The natural frequencies are obtained as a function of length scale parameter, rotational speed, inhomogeneity index, hub and taper parameter. It is found that FG-A and FG-X distribution of GNPs give maximum and minimum values of natural frequency, respectively.