Spectral element model for the vibration of a spinning Timoshenko shaft

Lee, Usik; Jang, Ik‐Soon

doi:10.2140/jomms.2012.7.145

Cited by 6 publications

(11 citation statements)

References 11 publications

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“…The spectral element matrix for a spinning shaft is available from Lee and Jang. 6 The nodal DOFs defined on the right and left surfaces of the disc can be related to each other as follows (2) r and using equation (8), we can assemble three spectral element equations given by equation (7) in the following form …”

Section: Equations Of Motion Of Interim Discmentioning

confidence: 99%

Frequency domain spectral element model of uniform spinning shafts with thick discs

Park

Lee

2014

Materials Research Innovations

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A frequency domain spectral element model is developed for a bearing supported rotor system, which consists of two spinning shafts and an interim disc. For the proposed spectral element model, the spinning shafts are represented by Timoshenko shaft models. The interim disc is represented by a uniform thick rigid disc with an unbalance mass, and it is considered to be wobbling about its geometric centre to which the spinning shafts are connected.

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Section: Equations Of Motion Of Interim Discmentioning

confidence: 99%

Frequency domain spectral element model of uniform spinning shafts with thick discs

Park

Lee

2014

Materials Research Innovations

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“…In works [4,5,7], the results of analytical solutions (natural frequency values) were used as reference data to verify the proposed FE models of discussed systems. A spectral element model for a spinning uniform shaft was developed in paper [8], and FEM analysis was used for evaluating the accuracy of the proposed model through some example problems. Shahgholi et al [9] discussed the issues of transverse vibrations of a slender shaft using analytical methods.…”

Section: Introductionmentioning

confidence: 99%

Analytical and Numerical Analysis of Injection Pump (Stepped) Shaft Vibrations Using Timoshenko Theory

Noga

Rejman

Bałon

et al. 2022

Acta Mechanica Et Automatica

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The free transverse vibrations of shafts with complex geometry are studied using analytical methods and numerical simulations. A methodology is proposed for evaluating the results of a natural transverse vibration analysis as generated by finite element (FE) models of a shaft with compound geometry. The effectiveness of the suggested approach is tested using an arbitrarily chosen model of the injection pump shaft. The required analytical models of the transverse vibrations of stepped shafts are derived based on the Timoshenko thick beam theory. The separation of variables method is used to find the needed solutions to the free vibrations. The eigenvalue problem is formulated and solved by using the FE representation for the shaft and for each shaft-simplified model. The results for these models are discussed and compared. Additionally, the usefulness of the Myklestad–Prohl (MP) method in the field of preliminary analysis of transverse vibration of complex shaft systems is indicated. It is important to note that the solutions proposed in this paper could be useful for engineers dealing with the dynamics of various types of machine shafts with low values of operating speeds.

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“…Thus, Timoshenko beam theory has been widely applied to shafts that spin at very high speeds [2][3][4][5], whereas interim disks have been represented by thin or thick rigid disks [6]. Historically, many analytical methods have been applied to the dynamics of rotor systems.…”

Section: Introductionmentioning

confidence: 99%

“…The SEM might have apparent advantages over other solution methods such as the transfer matrix method and the FEM, especially when it is applied to a 1D dynamic system such as a rotor system. Lee and Jang [5] and Lee [14] were the first to apply the SEM to the dynamic modeling and analysis of rotor systems represented by a spinning flexible Timoshenko shaft, with or without a mass-balanced interim disk. To the authors' knowledge, the SEM has not been applied to rotor systems that have interim disks with an unbalanced mass.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of Flexible Rotor Systems with an Interim Mass Unbalanced Disk Using a Spectral Element Model

Choi

Lee

2014

Mathematical Problems in Engineering

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A frequency domain spectral element model is developed for a rotor system that consists of two spinning shafts and an interim disk or blade system. In this study, the shafts are represented by spinning Timoshenko beam models, and the interim disk system is represented by a uniform thick rigid disk with an unbalanced mass. In our derivation of the governing equations of motion of the disk system, the disk is considered to be wobbling about the geometric center of the disk at which the spinning shafts are attached. The high accuracy of the proposed spectral element model is evaluated by comparison with the natural frequencies obtained using the conventional finite element method (FEM). The spectral element model is then used to investigate the effects of the unbalanced mass on the natural frequencies and dynamic responses of an example rotor system.

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Spectral element model for the vibration of a spinning Timoshenko shaft

Cited by 6 publications

References 11 publications

Frequency domain spectral element model of uniform spinning shafts with thick discs

Frequency domain spectral element model of uniform spinning shafts with thick discs

Analytical and Numerical Analysis of Injection Pump (Stepped) Shaft Vibrations Using Timoshenko Theory

Dynamics of Flexible Rotor Systems with an Interim Mass Unbalanced Disk Using a Spectral Element Model

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