Effect of radially functionally graded materials on the primary resonances of large amplitude flexural vibration of in-extensional rotating shafts

Abstract

This paper analytically studies the effect of functionally graded materials (FGMs) on the primary resonances of large amplitude flexural vibration of in-extensional rotating shafts with nonlinear curvature as well as nonlinear inertia. The constituent material is assumed to vary along the radial direction according to a power-law gradation. The governing differential equations and the corresponding boundary conditions are derived employing the variational approach. Then, the Galerkin method and the multiple scales perturbation method are utilized to obtain the frequency–response equation. In a numerical case study, the effects of the power-law index on the steady-state responses and locus of two saddle-node bifurcations for a heterogeneous functionally graded rotating shaft fabricated from the mixture of Aluminum oxide (Al2O3) and Stainless Steel (SUS304) are illustrated. The results of the present study are compared with the reported results for a homogeneous shaft as some kind of validation of the developed model. The results of this paper provide useful and practical information that can be helpful in the design of these new well-developed structures.