 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| A. P. Malyshev, "Simultaneous modeling of frequency-independent and viscous damping of vibrations," Mech. Solids. 39 (3), 133-139 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
3 |
Pages |
133-139 |
| Title |
Simultaneous modeling of frequency-independent and viscous damping of vibrations |
| Author(s) |
A. P. Malyshev (Moscow) |
| Abstract |
The vibration energy dissipation in mechanical systems and structures is frequently due to the structural damping. The absorption coefficient for the structural damping does not depend on the frequency but substantially depends on the amplitude. Such a behavior of the absorption coefficient is characteristic also of the energy loss in materials if the stresses are commensurable with the fatigue limit. For low-level vibrations, the damping with the absorption coefficient depending on the frequency is more pronounced, whereas the influence of the amplitude can be neglected. Frequently, this kind of damping can be taken into account by viscoelastic models. In the present paper, the aforementioned two kinds of damping are referred to as the frequency-independent damping and viscous damping. When investigating a broad range of vibration levels or considering vibrations with a broad excitation spectrum, it is necessary to take into account both kinds of energy loss simultaneously. This is especially important for modern structures from composite materials. We propose a differential model which takes into account both kinds of damping. This model applies for any distribution of dissipation forces and arbitrary time history of the load. The characteristics of this model are investigated for the forced vibrations of a single-degree-of-freedom system and longitudinal vibrations of a rod. Typical features of the frequency-independent damping are established. The influence of this damping on the vibration shape of the rod is estimated. |
| References |
| 1. | Ya. G. Panovko, Internal Friction in Vibrating Elastic Systems [in Russian], Fizmatgiz, Moscow, 1960. |
| 2. | G. S. Pisarenko, Energy Dissipation in Mechanical Vibrations [in Russian], Izd-vo AN USSR, Kiev, 1962. |
| 3. | A. P. Malyshev, "Numerical simulation of static and dynamic behavior of frameworks on a rough surface," Izv. AN. MTT [Mechanics of Solids], No. 4,
pp. 165-172, 2000. |
| 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. | N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel'kov,
Numerical Methods [in Russian], Nauka, Moscow, 1987. |
| 6. | S. K. Godunov, "A difference method for the numerical analysis of discontinuous solutions of equations of hydrodynamics,"
Matematicheskii Sbornik, Vol. 47, No. 3, pp. 271-306, 1959. |
|
| Received |
12 September 2001 |
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