<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

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

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The free transverse vibrations of shafts with complex geometry are studied using analytical methods and numerical simulations. A methodology is proposed for...

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

Published Online: Jul 01, 2022

Page range: 215 - 224

Received: Mar 29, 2022

Accepted: May 12, 2022

DOI: https://doi.org/10.2478/ama-2022-0026

Keywords
modal analysis, natural vibrations, analytical solutions, Timoshenko beam theory, shaft vibrations

© 2022 Stanisław Noga et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Jul 01, 2022

Page range: 215 - 224

Received: Mar 29, 2022

Accepted: May 12, 2022

DOI: https://doi.org/10.2478/ama-2022-0026

Keywordsmodal analysis, natural vibrations, analytical solutions, Timoshenko beam theory, shaft vibrations

© 2022 Stanisław Noga et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
modal analysis, natural vibrations, analytical solutions, Timoshenko beam theory, shaft vibrations