On the Critical Speeds of a Continuous Shaft-Disk System

Eshleman, R. L.; Eubanks, R. A.

doi:10.1115/1.3610126

Cited by 34 publications

(21 citation statements)

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“…From the foregoing literature reviews, one sees that all existing techniques for the analysis of whirling motions are the approximate approaches except for the analytical method presented by Eshleman and Eubanks [4] and that introduced by Yamamoto and Ishida [11]. In theory, the solution of Eshleman and Eubanks [4] is an exact one, however, it is only for the whirling speeds of a rotating shaft carrying "one" disk and the corresponding "whirling mode shapes" are not considered.…”

Section: Introductionmentioning

confidence: 99%

“…In theory, the solution of Eshleman and Eubanks [4] is an exact one, however, it is only for the whirling speeds of a rotating shaft carrying "one" disk and the corresponding "whirling mode shapes" are not considered. Thus, the purpose of this paper is to extend and modify the aforementioned technique, so that the lowest five (or higher) forward and backward whirling speeds and the associated mode shapes for a shaft carrying any number of disks with various boundary conditions can be easily obtained.…”

Section: Introductionmentioning

confidence: 99%

“…The existing literature reveals that the dynamic problems of rotor-bearing systems are solved by the step-by-step integration process [1], transfer matrix method (TMM) [2], analytical method [3][4][5], assumed mode method [6], hybrid method [7], frequency-dependent TMM [8] or the finite element method (FEM) [9,10]. Besides, Yamamoto and Ishida [11] have introduced the applications of the analytical methods, the TMM and FEM, to the linear and nonlinear dynamics of multidisk rotor-bearing systems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analytical Solution for Whirling Speeds and Mode Shapes of a Distributed-Mass Shaft With Arbitrary Rigid Disks

Wu¹,

Lin²,

Shaw

2013

Journal of Applied Mechanics

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The purpose of this paper is to present an approach for replacing the effects of each rigid disk mounted on the spin shaft by a lumped mass together with a frequency-dependent equivalent mass moment of inertia so that the whirling motion of a rotating shaft-disk system is similar to the transverse free vibration of a stationary beam and the technique for the free vibration analysis of a stationary beam with multiple concentrated elements can be used to determine the forward and backward whirling speeds, along with mode shapes of a distributed-mass shaft carrying arbitrary rigid disks. Numerical results reveal that the characteristics of whirling motions are significantly dependent on the slopes of the associated natural mode shapes at the positions where the rigid disks are located. Furthermore, the results obtained from the presented analytical method and those obtained from existing literature or the finite element method (FEM) are in good agreement.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical Solution for Whirling Speeds and Mode Shapes of a Distributed-Mass Shaft With Arbitrary Rigid Disks

Wu¹,

Lin²,

Shaw

2013

Journal of Applied Mechanics

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“…In general, the question of critical speeds of rotor systems has been addressed by many authors [5,[19][20][21]. The frequency equations and critical speeds of a straight circular rotor were obtained by Eshleman and Eubanks [5] who included the transverse shear, rotatory inertia and gyroscopic moments together with continuous shaft effects (distributed mass and elasticity) in their model.…”

Section: Introductionmentioning

confidence: 99%

“…The frequency equations and critical speeds of a straight circular rotor were obtained by Eshleman and Eubanks [5] who included the transverse shear, rotatory inertia and gyroscopic moments together with continuous shaft effects (distributed mass and elasticity) in their model. Research on rotor dynamics over the past three decades has been on improved models with the expedient of finite element formulation in some cases [6,[8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Evolution of whirl in flexible isotropic rotors : modelling and experimental study

2017

IJLTET

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An efficient approach for whirling speeds and mode shapes of uniform and nonuniform Timoshenko shafts mounted by arbitrary rigid disks

Hsu

2020

Engineering Reports

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In theory, the whirling motion of a shaft-disk system is three-dimensional (3D), however, if the transverse displacement in the vertical principal xy-plane and that in the horizontal principal xz-plane for the cross-section of the shaft located at the axial coordinate x are represented by a complex number, then the mass moment of inertia for unit shaft length (at x) and that for each rigid disk i can be combined with their associated gyroscopic moments (GMs) to form the frequency-dependent equivalent mass moments of inertia, respectively, in the equations of motion for the rotating Timoshenko shaft carrying arbitrary rigid disks. It is found that the above-mentioned equations for the rotating 3D shaft-disk system take the same forms as the corresponding ones for the associated stationary two-dimensional (2D) Timoshenko beam carrying the same number of disks, so that the approaches for the free vibration analyses of the stationary 2D beam-disk system can be used to solve the title problem for obtaining the whirling speeds and mode shapes of a rotating 3D shaft-disk system. Since the order of the eigenproblem equation derived from the presented approach is much smaller than that derived from the conventional finite element method (FEM), the computer time consumed by the former is much less than that by the latter. In addition, the solutions obtained from the presented approach are exact and may be the benchmark for evaluating the accuracy of solutions of the other approximate methods. Numerical examples reveal that the presented approach is available for the uniform or nonuniform shaft-disk system, and the obtained results are very close to those obtained from existing literature or the FEM. The formulation of this article is available for a shaft-disk system with various boundary conditions (BCs), to save space, only the cases with pinned-pinned BCs are illustrated. K E Y W O R D S Timoshenko shaft, gyroscopic moment, equivalent mass moment of inertia, whirling speeds and mode shapes This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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On the Critical Speeds of a Continuous Shaft-Disk System

Cited by 34 publications

References 0 publications

Analytical Solution for Whirling Speeds and Mode Shapes of a Distributed-Mass Shaft With Arbitrary Rigid Disks

Analytical Solution for Whirling Speeds and Mode Shapes of a Distributed-Mass Shaft With Arbitrary Rigid Disks

Evolution of whirl in flexible isotropic rotors : modelling and experimental study

An efficient approach for whirling speeds and mode shapes of uniform and nonuniform Timoshenko shafts mounted by arbitrary rigid disks

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