 | | 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: | | 12854 |
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| In English (Mech. Solids): | | 4810 |
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| S. E. Zaitsev and O. N. Tushev, "Estimation of the influence of random additive and multiplicative vibrations on the dynamic behavior of a system," Mech. Solids. 36 (6), 140-143 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
6 |
Pages |
140-143 |
| Title |
Estimation of the influence of random additive and multiplicative vibrations on the dynamic behavior of a system |
| Author(s) |
S. E. Zaitsev (Moscow)
O. N. Tushev (Moscow) |
| Abstract |
The influence of high-frequency random vibrations of different nature
(additive and parametric) on the "slow motion" of a system is
analyzed. The system with suspension and other elements can be
described by an ordinary vector differential equation. It is
assumed that external stationary or nonstationary excitations are
defined within the framework of the correlation theory.
The solution is sought by representing the vector of phase
coordinates of the system as the integro-power series with respect
to the matrix containing the random vibrations. Confining
ourselves to the quadratic approximation for the multiplicative
components, we obtain the convenient explicit function of
the entries of the correlation matrix of vibrations, which permits
us to analyze the contribution of each vibration component into the
dynamic behavior of the system.
The results are illustrated by an example.
The influence of high-frequency additive and parametric vibrations
on a dynamic system has been thoroughly studied. A typical example of this
effect is the shift of a pendulum as a result of fast sinusoidal
vibration of the suspension. To describe this effect, the Mathieu
or Hill equations with right-hand side are usually used.
Similar results are obtained for random stationary vibrations.
Thus, for simple systems and stationary vibrations, this effect is
easy to describe qualitatively and quantitatively. Considerable
difficulties arise for a system with many degrees of freedom
subjected to several random stationary or nonstationary excitations
(the last case involves much more difficulties).
The problem considered in the present paper is of particular
importance for protecting some mechanical objects,
such as measuring devices, from vibrations. Vibrations may not lead to
catastrophic results (for example, accelerations and displacements
lie within their acceptable limits with large margins of safety),
but substantially affect the functional properties of devices.
This effect usually manifests itself in the appearance of a
spurious signal. The magnitude of this signal essentially depends on
the adjustment of the damping system. For the purposes of design, it
is important not only to define the spurious signal, but also to
evaluate the contribution of each vibration component to this signal. |
| References |
| 1. | F. G. Gantmakher, Theory of Matrices [in Russian], Nauka,
Moscow, 1967. |
| 2. | R. Bellman, Introduction to the Theory of Matrices [Russian
translation], Nauka, Moscow, 1969. |
| 3. | V. N. Chelomei (Editor), Vibrations in Engineering [in
Russian], Mashinostroenie, Moscow, 1981. |
|
| Received |
06 October 1999 |
| << Previous article | Volume 36, Issue 6 / 2001 | Next article >> |
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