Large amplitude vibration of rotating graphene reinforced titanium alloy dovetailed blades with general boundary conditions

Abstract

Engine blades are generally installed on disks via dovetail joints, which can alleviate stress concentrations at the blade root and prevent heat transfer. As a result, the connection stiffness is strongly affected by the clearance between the blade and disk as well as the rotation speed of the blade. This paper first proposes a functionally graded graphene-reinforced titanium alloy trapezoid plate with elastic boundary conditions to investigate the large amplitude vibration of rotating dovetailed blades. The elastic boundaries are modelled by applying a series of artificial springs, and the related admissible displacement functions are constructed by orthogonal polynomials through the Gram–Schmidt process. The governing equations of the functionally graded graphene platelet reinforced composite (FG-GPLRC) trapezoid plate are derived by the first-order shear deformation theory (FSDT) and Lagrange equation. The numerical results of the large amplitude vibration of the plate are obtained by the weighted residual method combined with a direct iterative algorithm and verified through analytical solutions of the harmonic balance method. The effects of the stiffness of the constraint springs, rotation speed and structural parameters on the linear and nonlinear free vibrations of the FG-GPLRC trapezoid plate are thoroughly studied.