International Journal of Mechanical Engineering and Applications

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Stable Equilibrium of a Mechanical Energy Storage Device

This study determines the energy of a fatigue-loaded shaft of circular cross-section, in stable equilibrium, deflecting during rotation even in the absence of external loads. The shaft is subjected to completely reversed stresses as well as torsion and bending stresses varying with rotation and introducing fatigue loading problems. The research was conducted in order to establish equilibrium condition at which a shaft subjected to fatigue loading can operate without axial vibration problems, divergence buckling, and instability at critical or above critical speeds. When inertia slows the shaft to rest, where the energy goes usually causes the shaft to rattle. At rest, kinetic energy is zero at that point while potential energy is maximum. The stability status of the shaft can eliminate rattling. The energy method is used, in this study, to develop force-displacement relations. It is also used to show that the total potential energy is minimum in the rotating shaft. Invoking the principle of minimum potential energy is a way to more easily derive the shaft energy related characteristics. The principle is used to analyze displacement and end points boundary conditions. Boundary conditions give prescription of displacements. The principle of virtual displacements and that of the minimum potential energy give the so-called stiffness (or displacement) method. The primary unknowns in that are the nodal displacements instead of the nodal forces. The strain-energy-density factor represents the strength of the elastic energy field in the vicinity of a crack-tip (with stress singularity) developed in the shaft. It was found that the energy which is a source of fluctuation in motion during shaft rotation was minimum when the total energy transferred to the shaft is minimum.

Stiffness, Strain Energy, Minimum Potential Energy, Fatigue, Torsion

Steven Odi-Owei, Kenny Ayoka. (2023). Stable Equilibrium of a Mechanical Energy Storage Device. International Journal of Mechanical Engineering and Applications, 11(3), 60-65.

Copyright © 2023 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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