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The influences of stagger angle (α) and pretwist angle (βL) of blades on the coupling vibration among shaft bending and blade bending in a shaft-disk-blade (SDB) system are investigated using a Lagrangian approach in combination with the assumed modes method (AMM). The disk is rigid, and the flexible shaft is supported with two rigid bearings. It is shown that α and βL have variable effects on the coupling vibration because their influences can be increased, reduced, or even completely eliminated for different values of disk location (λ), blade thickness ratio (δ), and blade aspect ratio (γ). To study the coupling vibration in an SDB system, consideration of λ, δ, and γ are very important because those can alter the coupling magnitude, the coupling pattern as well as the predominant modes. Nevertheless, previous researches rarely take into account these parameters. Moreover, in the present work, to investigate the natural frequencies and critical speeds versus λ, δ, and γ, new diagrams are introduced. Also, the relation between the in-plane and out-of-plane motions of the blades with the coupling vibration is precisely analyzed.