Free vibration and dynamic stability of functionally graded composite microtubes reinforced with graphene platelets

This paper studies the free vibration and dynamic stability characteristics of functionally graded composite multilayer microtubes reinforced with graphene platelets under axial mechanical load. The graphene platelets are assumed to be uniformly or gradiently distributed across the radial direction of the microtube, and the corresponding effective material properties are estimated by the modified Halpin-Tsai model and the rule of mixture. Based on the modified couple stress theory and a refined higher-order beam theory, a size-dependent multilayer tube model for the dynamic analysis is developed. By employing Hamiltons principle, the governing equations and associated boundary conditions are derived. Galerkin technique is applied to convert the governing partial differential equations into ordinary ones, from which the analytical solutions of natural frequencies and dynamic instability regions under different boundary conditions can be obtained. After verifying the accuracy of the proposed model, the influences of graphene platelets distribution pattern and weight fraction, microstructure effect, axial load as well as geometrical parameters on the free vibration and dynamic stability behaviors of functionally graded composite multilayer microtubes are investigated. It is found that distributing more graphene platelets in the outer layers but fewer in the inner layers has the best reinforcing effect for the composite microtubes.