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

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


Releases Archive. Вестник ТюмГУ. Физико-математические науки. Информатика (№7, 2013)

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

About the authors:

Sergey P. Pirogov, Dr. Techn. Sci., Professor, Department of applied mechanics, Tyumen State Oil and Gaz University
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.


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.


1. Pirogov, S.P., Chuba, A.Ju. Calculation of proper oscillation frequency of manometric tubular springs. Izvestija vuzov. Priborostroenie — Proceedings of Institutions of Higher Education. Instrument Engineering. 2012. №1. Pp. 39-43. (in Russian).

2. Pirogov, S.P., Chuba, A.Ju. Comparative analysis of manometric springs models. Vestnik Tjumenskogo gosudarstvennogo universitet — Tyumen State University Herald. №4. 2012, Pp. 114-118. (in Russian).

3. Getc, A.Ju., Dolgushin, Ju.S., Machkinis, V.I., Chuba, A.Ju., Pirogov, S.P., Smolin, N.I. Experimental research on proper oscillation frequency of manometric springs. Izvestija vysshih uchebnyh zavedenij. Neft' i gaz. — Proceedings of Institutions of Higher Education. Oil and Gas. 2008. №2. Pp. 105-107. (in Russian).

4. Gridnev, M.P. Issledovanie i razrabotka manometricheskogo pribora, ustojchivogo v uslovijah vibracii i pul'sacii davlenija (diss. kand.) [Design and development of a manometric device, resistant to oscillation and pulse pressure (Cand. Diss.)]. Tomsk,, 1969. 18 p. (in Russian).

5. Rabotnov, Ju.N. Mehanika deformiruemogo tverdogo tela: Ucheb. posobie dlja vuzov [Mechanics of rigid body deformation. Textbook for colleges]. M.: Nauka, 1988. 712 p.

(in Russian).

6. Nikitin, N.N. Kurs teoreticheskoj mehaniki [Theoretical Mechanics]. M.: Vysshaja shkola, 1990. 607 p. (in Russian).

7. Biderman, V.L. Teorija mehanicheskih kolebanij [Mechanic oscillation theory]. M.: Vysshaja shkola, 1980. 408 p. (in Russian).

8. Vibracii v tehnike: Spravochnik. V 6-ti t. / Red. V.N. Chelomej. T.3. Kolebanija mashin, konstrukcij i ih jelementov / Pod red. F.M. Dimentberga i K.S. Kolesnikova [Oscillation in technics: Reference book. 6 volumes / Edited by V.N. Chelomei. V. 3. Oscillation of machines, oscillation and their components / Edited by F.M. Dimentberg and K.S. Kolesnikova]. M.: Mashinostroenie, 1980. 544 p. (in Russian).

9. Arsenin, V.Ja. Metody matematicheskoj fiziki i special'nye funkcii. 2-e izd., pererabot. i dop. [Mathematical physics methods and particular functions. 2d edition, revised]. М.: Nauka, 1984. 384 p. (in Russian).

10. Kalitkin, N.N. Chislennye metody [Calculus of approximations]. M.: Nauka,, 1978. 200 p. (in Russian).

11. Mihlin, S.G. Variacionnye metody v matematicheskoj fizike [Variation methods in mathematical physics]. M.: Nauka, 1970. 512 p. (in Russian).