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.
In this paper we consider a regularized least squares problem subject to convex constraints. Our algorithm is based on the superiorization technique, equipped with a new step size rule which uses subgradient projections. The superiorization method is a two-step method where one step reduces the value of the penalty term and the other step reduces the residual of the underlying linear system (using an algorithmic operator T ). For the new step size rule, we present a convergence analysis for the case when T belongs to a large subclass of strictly quasi-nonexpansive operators. To examine our algorithm numerically, we consider box constraints and use the total variation (TV) functional as a regularization term. The specific test cases are chosen from computed tomography using both noisy and noiseless data. We compare our algorithm with previously used parameters in superiorization. The T operator is based on sequential block iteration (for which our convergence analysis is valid) but we also use the conjugate gradient method (without theoretical support). Finally we compare with the well-known 'fast iterative shrinkage-thresholding algorithm' (FISTA). The numerical results demonstrate that our new step size rule improves previous step size rules for the superiorization methodology and is competitive with, and in several instances behaves better than, the other methods.
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