Науковий вісник НГУ

Sectional shape of a flexible body sliding over a fixed block

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Category: Geotechnical and mining mechanical engineering, machine building

Last Updated on 04 February 2016

Published on 04 February 2016

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Authors:

N.A. Lubenets, Cand. Sci. (Tech.), Associate Professor, State Higher Educational Institution “National Mining University”, Senior Lecturer of the Department of Transport Systems and Technology, Dnipropetrovsk, Ukraine

Abstract:

Purpose. To derive a solution of classical Euler problem about a flexible body sliding over a fixed block taking into account the cross-sectional shape of the real flexible solid body.

Methodology. We determined the location of the neutral layer of the real flexible solid body of an arbitrary shape of cross-section, extended in the dimension of longitudinal stress application and solved a flexible body sliding over a fixed block taking into account the shape of cross-section of the real flexible solid body.

Findings. We set the radius of curvature of the neutral layer of the flexible body along the line of contact with the block, extended along longitudinal tension force. The layer of the flexible body influenced by the resultant tension force. We derived the differential equation of equilibrium of the friction force, tension force of the flexible body and obtained a new solution of the classical Euler problem about a flexible body sliding over a fixed block.

Originality. For the first time, we substantiated the quantitative model of the real flexible solid body, including the definition of the radius of curvature of the neutral layer influenced by the resultant tension force of the flexible body. The research presents the solution of the classical Euler problem about a flexible body sliding over a fixed block considering the law of conservation of mechanical energy and current knowledge on solids friction.

Practical value. Quantitatively, we introduced the amendment to the solution of the Euler problem about a flexible body sliding over a fixed block considering the real shape of the section of the flexible body. The knowledge gained contribute to the understanding of the process of friction of flexible solid bodies.

References:

1. Лубенец Н.А. Влияние центробежных сил гибкого тела на реализацию тягового усилия трением / Н.А. Лубенец, Т.Н. Лубенец // Науковий вісник НГУ. – Дніпропетровськ, 2012. − № 5. – С. 28–33.

Lubenets N., Lubenets T. (2012), “Effect of centrifugal forces of a flexible body on traction friction implementation”, Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, no.5, pp. 28−33.

2. Кирия Р.В. Применение метода возмущений Л. Прандтля к разрешению парадокса Н.Е. Жуковского / Р.В. Кирия, Е.А. Стаховский // Системні технології. – Днепропетровск, 2002. – № 4 (21). − С. 33–46.

Kiriya R.V. and Stakhovsky, Ye.A. (2002), “The use of the perturbation method of L. Prandtl to resolve the paradox of N.Ye. Zhukovsky”, Systemnі Tekhnolohii, Dnepropetrovsk, no. 4(21), pp. 33−46.

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