 | | 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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| M. Ya. Izrailovich, "Controlled excitation of self-induced vibrations with parametric and force type sources," Mech. Solids. 37 (3), 42-50 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
3 |
Pages |
42-50 |
| Title |
Controlled excitation of self-induced vibrations with parametric and force type sources |
| Author(s) |
M. Ya. Izrailovich (Moscow) |
| Abstract |
Controlled excitation of self-induced vibrations in a one-dimensional
mechanical system with lumped nonlinearity is considered.
Vibrations of the system are excited by sources of two types-
parametric and force, the characteristics of both these sources
depending on the coordinate and velocity. We assume that the prescribed
frequency of self-induced vibrations corresponds to either resonant or
filtering properties of the passive part of the system and that the first
harmonic approximation to the solution of the governing equation provides
an acceptable accuracy. In this case, one can obtain the excitation
conditions in closed form by combining the harmonic linearization with
variational methods. The possibility of sustaining stable self-induced
vibrations of high intensity is illustrated for specific cases.
The utilization of methods of the control theory for the synthesis
of self-vibrating systems was considered in [1-4] for the case
of force excitation and in [5,6] for the case of parametric excitation.
However, the most promising approach to the design of new high-efficiency
generators of self-induced vibrations involves combined utilization
of the parametric-type and force-type excitation sources. Due to multiplicative
interaction of two controlled exciting factors, such systems allow generating
substantially more intensive vibrations, as compared with systems equipped
with the excitation source of only one type. Moreover, unlike systems with only
parametric excitation, systems with combined excitation can generate
stable vibrations in the cases where the generation of such vibrations
is impossible without controlled force excitation (this is the case, for example,
for systems with linear passive parts). |
| References |
| 1. | A. V. Repnikov, Vibrations in Optimal Systems of Automatic Control
[in Russian], Mashinostroenie, Moscow, 1968. |
| 2. | A. A. Krasovskii, "Synthesis of self-vibrating systems
with application to wind-driven power plants of new class,"
Izv. AN. Tekhnicheskaya Kibernetika, No. 6, pp. 5-15, 1994. |
| 3. | M. Ya. Izrailovich and N. I. Morozova, "Optimal control
of periodic motions of single-degree-of-freedom mechanical systems,"
Mashinostroenie, No. 2, pp. 39-46, 1981. |
| 4. | M. Ya. Izrailovich, "Control of self-induced vibrations
in resonant systems," Izv. AN. Teoriya i Sistemy Upravleniya,
No. 6, pp. 55-65, 1995. |
| 5. | M. Ya. Izrailovich, "Synthesis of self-vibrating systems
with parametric excitation," Problemy Mashinostroeniya i Nadezhnosti
Mashin, No. 4, pp. 20-28, 1996. |
| 6. | M. Ya. Izrailovich, "Parametric excitation
of self-oscillations," Izv. AN. MTT [Mechanics of Solids],
No. 3, pp. 54-63, 1997. |
| 7. | E. P. Popov, Applied Theory of Control Processes in Nonlinear
Systems [in Russian], Nauka, Moscow, 1973. |
|
| Received |
30 December 1999 |
| << Previous article | Volume 37, Issue 3 / 2002 | Next article >> |
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