 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 37, Issue 2 / 2002 | Next article >> |
| V. G. Veretennikov and V. A. Sinitsyn, "Analysis of the dynamical model of the system rigid wheel-deformable rail," Mech. Solids. 37 (2), 39-46 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
2 |
Pages |
39-46 |
| Title |
Analysis of the dynamical model of the system rigid wheel-deformable rail |
| Author(s) |
V. G. Veretennikov (Moscow)
V. A. Sinitsyn (Moscow) |
| Abstract |
The rolling of a rigid body along a deformable elastic rail
lying on a viscoelastic foundation is studied. Earlier [1, 2],
the approximate Bernoulli-Euler theory has been used to construct
the model of this system.
In the present paper, we utilize
Timoshenko's theory of beam bending. In the kinetic energy functional,
we take into account the inertial properties of cross-sections
of the beam. The dissipative forces are accounted for in accordance
with Rayleigh's theory. Constraints, treated as ideal constraints,
are analyzed. The Hamilton principle is utilized to derive the equations
of motion. The constraint forces determined quantitatively characterize
the physical properties of the process, such as the appearance of additional
shear forces in the beam's cross-sections and the reaction in the place
of contact, including the rolling resistance torque. The creep
phenomenon has been identified for transverse deformations. New values
of the critical velocities are determined and a modified equation of
the rail neutral axis was found for the case of steady rolling of
the wheel. |
| References |
| 1. | S. P. Timoshenko, Strength and Vibration of Structural Members:
Selected Works [Russian translation], Nauka, Moscow, 1975. |
| 2. | V. G. Vil'ke, "On the rolling of a rigid wheel along a deformable
rail," PMM [Applied Methematics and Mechanics],
Vol. 59, No. 3, pp. 512-517, 1995. |
| 3. | V. L. Berdichevskii, Vatiational Principles in Continuum Mechanics
[in Russian], Nauka, Moscow, 1983. |
| 4. | L. E. El'sgol'ts. Differential Equations and Calculus of Variations
[in Russian], Nauka, Moscow, 1969. |
| 5. | E. S. Sorokin, To the Theory of Internal Friction in Vibrations
of Elastic Systems [in Russian], Gosstroiizdat, Moscow, 1960. |
| 6. | V. V. Rumyantsev, "On the integral principles for nonholonomic
systems," PMM [Applied Methematics and Mechanics],
Vol. 46, No. 1, pp. 3-12, 1982. |
| 7. | M. V. Ostrogradskii, "A note on the equilibrium of an elastic
thread," in M. V. Ostrogradskii. Complete Works [in Russian], Vol. 1,
pp. 116-117, Izd-vo AN UkrSSR, Kiev, 1959. |
| 8. | A. P. Filatov, Vibration of Deformable Systems [in Russian],
Mashinostroenie, Moscow, 1970. |
| 9. | Y. Rocard, L'Instabilite en Mechanique. Automobiles. Avions.
Ponts Suspendus, Masson, Paris, 1954. |
|
| Received |
21 March 2000 |
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