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


Release:

Releases Archive. Вестник ТюмГУ. Физико-математические науки. Информатика (№7, 2014)

Title: 
Mathematical model of manometric spring in a viscous medium


About the authors:

Dmitry A. Cherentsov, Post-graduate student, Assistant Lecturer, Department of Hydrocarbons Transport, Tyumen State Oil and Gas University
Sergey P. Pirogov, Dr. Techn. Sci., Professor, Department of applied mechanics, Tyumen State Oil and Gaz University
Sergey M. Dorofeyev , Associate Professor, Department of Mathematics and Information Science, Tyumen State University, Cand. Phys. and Math. Sci.

Abstract:

A mathematical model of the manometric tube spring located in the fluid is presented in the article. The model allows to calculate the parameters of damped oscillations of the springs. To improve the accuracy of measurement, the geometric parameters of manometric tube springs are changed by raising their vibration fatigue. Alternatively, it is possible to immerse manometric tube springs into the liquid damping vibrations. Vibration damping depends on the damping coefficient and the frequency of damping vibrations. Thus, there is a need to determine them. A dynamic model of the manometric tube spring is presented in the form of thin-walled curved rod which oscillates in the plane of curvature of the central axis. Fluid resistance is represented as a distributed load. Element wave equations are obtained in accordance with the principle of d’Alamber in the projections on the normal and tangential. Boundary conditions: tangent and normal displacements, a rotation angle of the tube cross section in the section of rigid spring fixing is zero. At the opposite end, the bending moment, tensile forces and shear force go to zero. Bubnov-Galerkin method is used to solve the obtained equations.

References:

1. Pirogov, S.P. Manometricheskie trubchatye pruzhiny [Manometric tube springs]. St-Petersburg, 2009. 276 p. (in Russian).

2. Beljaev, N.M. Soprotivlenie materialov [Strength of materials]. Moscow: Nauka, 1965.

(in Russian).

3. Chuba, A.Ju. Raschet sobstvennyh chastot kolebanij manometricheskih trubchatyh pruzhin (kand. diss.) [Calculation of oscillation frequencies of manometric tube springs (Cand. Sci. (Tech.) Diss.)]. Tyumen, 2007. 137 p. (in Russian).

4. Kalitkin, N.N. Chislennye metody [Numerical methods]. Moscow: Nauka, 1978. 200 p.

(in Russian).

5. Fletcher, K. Chislennye metody na osnove metoda Galerkina [Computations Galerkin Methods with 107 figures]. Moscow, 1988. 352 p. (in Russian).

6. Biderman, V.L. Teorija mehanicheskih kolebanij [Theory of mechanical vibrations]. Moscow, 1980. 480 p. (in Russian).

7. Timoshenko, S.P. Kolebanija v inzhenernom dele [Engineering vibrations]. Moscow: Nauka, 1967. 444 p. (in Russian).

8. Smirnov, V.I. Kurs vysshej matematiki. T. 2 [A course of higher mathematics. Vol. 2]. Moscow: Nauka, 1957. 420 p. (in Russian).

9. Kurosh, A.G. Kurs vysshej algebry. 11-e izd. [A course of higher algebra. 11th ed.]. Moscow: Nauka, 1975. (in Russian).

10. Jablonskij, A.A., Norejko, S.S. Kurs teorii kolebanij [A course of the oscillations theory]. St-Peterburg, 2003. 254 p. (in Russian).