Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2004-4pp.128-133

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A. P. Malyshev, "Modeling of the structural damping depending on the mean stress in a cycle," Mech. Solids. 39 (4), 128-133 (2004)
Year 2004 Volume 39 Number 4 Pages 128-133
Title Modeling of the structural damping depending on the mean stress in a cycle
Author(s) A. P. Malyshev (Moscow)
Abstract A model is suggested for taking into account the distributed structural damping, which is independent of the frequency of vibrations but depends on the amplitude and mean stress in a cycle. The relationship between the parameters of this model and the energy dissipation is analyzed. The model can be used for calculating dynamic modes with any time history of deformation of the structure. As an example, the transient processes in a rod subjected to instantaneous application and removal of an axisymmetric load are considered.

When studying the structural damping, one usually considers the relative displacement of the contact surfaces of connected elements and analyze the energy dissipation due to the external friction on these surfaces. Such problems can be solved only for a set of simple joints and structures, including laminated structures [1-5], which restricts the scope of objects that can be studied. The analysis of the dynamics of complex multi-component objects is often associated with calculation schemes with distributed parameters in which separate structural elements and components are spread. In these cases, to take into account damping, it is natural to use the model of internal energy dissipation in a material with reduced characteristics.

To describe the energy losses in materials, quite many models have been developed, which can describe not only vibrations close to harmonic, but also complex dynamic processes [1, 2, 6-8]. However, all these models are primarily effective for weak damping. They do not take into account the mean stress in the cycle, the corresponding decrement of vibrations tending to zero for small amplitudes. Such limitations are insignificant in considering the energy dissipation in most structural materials, particularly in metals. However, the results of dynamic tests show that these models are not applicable for the structural damping in complex structures. In such structures, the decrement of vibrations is rather high- from 10 to 20%- even for small amplitudes. Moreover, preliminary static loading or nonzero mean stress in the cycle considerably influence the duration and propagation of vibrations. Note that such effects are observed in many modern composite materials of complex structure.
1.  Ya. G. Panovko, Internal Friction in Vibrations of Elastic Systems [in Russian], Fizmatgiz, Moscow, 1960.
2.  K. V. Frolov (Editor), Vibrations in Engineering. Handbook. Volume 6 [in Russian], Mashinostroenie, Moscow, 1995.
3.  L. V. Nikitin, Statics and Dynamics of Solids With External Dry Friction [in Russian], Mosk. Litsei, Moscow, 1998.
4.  A. P. Malyshev, "Modeling of distributed structural damping for steady-state and transient processes," Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 143-150, 2001.
5.  A. P. Malyshev, "Longitudinal vibrations of a double-layer rod with displacement-dependent dry friction between the layers," Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 131-136, 2002.
6.  G. S. Pisarenko, Generalized Nonlinear Model for Taking Into Account Energy Dispersion in Vibrations [in Russian], Naukova Dumka, Kiev, 1985.
7.  A. P. Malyshev, "Differential model of the frequency-independent energy dissipation in vibrations," PMM [Applied Mathematics and Mechanics], Vol. 66, No. 1, pp. 127-133, 2002.
8.  A. P. Malyshev, "Constructing the model of the frequency-independent damping by using the amplitude characteristics of the damping coefficient," PMM [Applied Mathematics and Mechanics], Vol. 67, No. 1, pp. 134-141, 2003.
9.  S. D. Ponomarev (Editor), Strength Analysis in Mechanical Engineering. Volume 1 [in Russian], Mashgiz, Moscow, 1956.
10.  S. K. Godunov, "A difference method for numerical calculation of the discontinuous solutions of the equations of hydrodynamics," Mat. Sb., Vol. 47, No. 3, pp. 271-306, 1959.
Received 18 March 2003
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