A mathematic model of manometric tubular spring motion with respect of the mass of the rigid point

About the authors:

Sergey P. Pirogov, Dr. Sci. (Tech.), Professor, Professor of the Department of Applied Mechanics, Industrial University of Tyumen, Tyumen, Russia; Professor of the Department of Forestry, Woodworking and Applied Mechanics, Northern Trans-Ural State Agricultural University, Tyumen, Russia; piro-gow@yandex.ru, https://orcid.org/0000-0001-5171-8942

Aleksander Y. Tchuba, Cand. Techn. Sci., Associate Professor, Department of alltechnical disciplines, Tyumen state agricultural academy
Sergey M. Dorofeyev , Associate Professor, Department of Mathematics and Information Science, Tyumen State University, Cand. Phys. and Math. Sci.

Abstract:

The article contains a mathematic model of manometric tubular spring, which is used to calculate proper oscillation frequency of these spring with respect to the mass of the rigid point. Experimental studies of proper oscillation frequency of tubular springs with various wall thickness have shown the deviations of calculated values from experimental. It canbe explained by the rigid point, which is welded to the end of the tube, and the mass of the rigid point largely interferes with the proper oscillation frequencies of the spring. So, it is necessary to account for the mass of the rigid point when calculating proper oscillation frequency of manometric tubular springs. The tubular spring is described as a bent rod moving in the curvature plain of the central axis. One end of the rod is rigidly fixed and the other end is rigidly loaded. The equation models for a tubular element motion were obtained for normal and tangent projections in line with the D'Alembert's principle (which allows for the inertial forces). To take into account the mass of the point, the density of the string is considered changeable throughout the whole length — at the bedding point of the load it increases intermittently by a certain value. At the section of the rigid string fixture plane the tangent and normal transitions aa well as the angle of rotation of tubular cross-section are equal to zero, and at the free (opposite) end the bending moment, cutting and tensile strains are equal to zero, too.

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