 | | 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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| A. P. Malyshev, "Longitudinal vibrations of a double-layer rod with displacement-dependent dry friction between the layers," Mech. Solids. 37 (5), 110-114 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
5 |
Pages |
110-114 |
| Title |
Longitudinal vibrations of a double-layer rod with displacement-dependent dry friction between the layers |
| Author(s) |
A. P. Malyshev (Moscow) |
| Abstract |
A model is proposed for elastic-friction interaction between layers,
with dry friction force related to the relative displacements of the layers
by a power law. The model is subjected to parametric analysis.
Numerical results were obtained on the basis of the Godunov scheme.
In order to reduce the grid viscosity, the scheme is supplemented with
a nonuniform calculation of the discontinuity decay depending on
the current observation time.
The double-layer rod with elastic-friction interaction between the layers
is not only a fairly common structural element but also a convenient
computational model for the investigation of dynamical processes in rods
made of fiber-reinforced composites, cables, threads, etc. Inelastic
properties of such bodies are often described by linear rheological models,
which are fairly effective as applied to slow processes with the
characteristic time of the parameter variation being several seconds or
more [1-2]. However, these models have a very limited application for the
description of vibration damping, since the corresponding damping
decrement substantially depends on the frequency and is independent of
the amplitude, which, as a rule, contradicts the
experimental data. Although many dynamic problems can be studied on the
basis of the simplest dry friction Amonton-Coulomb model, this model
fails in the case of resonance modes [3].
The energy losses due to dissipation in all objects mentioned above
are caused primarily by friction forces which arise on
contact surfaces as separate threads, wires, or fibers slip against each
other. The simplest computational model which takes into account such
interactions is provided by a double-layer rod. |
| References |
| 1. | G. N. Kukin, A. N. Solov'ev, and A. I. Koblyakov,
Textile Materials Science [in Russian], Legprombytizdat, Moscow, 1989. |
| 2. | F. Scardino, G. Hirl, S. Kawabata, et al.,
Weaved Structural Composites [Russian translation],
Mir, Moscow, 1991. |
| 3. | L. V. Nikitin,
Statics and Dynamics of Solids with External Dry Friction [in Russian],
Mosk. Litsei, Moscow, 1998. |
| 4. | S. K. Godunov,
"A finite-difference method for discontinuous solutions of equations
in hydrodynamics," Matem. Sb., Vol. 47, No. 3, pp. 271-306, 1959. |
| 5. | A. P. Malyshev,
"Modelling of distributed structural damping for steady-state and
transient processes," Izv. AN. MTT [Mechanics of Solids], No. 4,
pp. 143-150, 2001. |
| 6. | Ya. G. Panovko,
Internal Friction in Vibrations of Elastic Systems [in Russian],
Fizmatgiz, Moscow, 1960. |
|
| Received |
20 September 2000 |
| << Previous article | Volume 37, Issue 5 / 2002 | Next article >> |
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