 | | 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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| I. V. Mishustin and L. S. Rybakov, "Vibrations of plane elastic orthogonal frameworks," Mech. Solids. 38 (2), 137-148 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
2 |
Pages |
137-148 |
| Title |
Vibrations of plane elastic orthogonal frameworks |
| Author(s) |
I. V. Mishustin (Moscow)
L. S. Rybakov (Moscow) |
| Abstract |
In [1-4], the matching method was used to
construct closed structural theories for a number of regular and
quasi-regular plane truss-type frameworks. Those theories can
be used when stating and solving a wide range of static problems for
such systems.
In the present paper, this approach is extended to problems of small
vibrations of plane elastic frameworks of orthogonal structure, the
internal friction being taken into account by the Voigt model.
Special attention is given to vibrations of a truss
formed by rectangular elementary cells with two diagonal beams
that do not interact at their intersection.
By removing a ceratin group of beams from such a framework,
it is possible to obtain a fairly wide class of regular, quasi-regular, and even
non-regular frameworks with an orthogonal structure.
We first give a rigorous
statement of the general problem of small vibrations of a framework,
and then this statement
is realized in detail for the problem of free vibrations without internal friction and
the problem of forced vibrations with internal friction. Both problems are illustrated
by numerical examples. |
| References |
| 1. | L. S. Rybakov,
"On the theory of a plane regular elastic structure of framework type,"
Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 171-179, 1995. |
| 2. | L. S. Rybakov, "Elastic analysis of a plane regular beam
structure," Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 198-207, 1996. |
| 3. | L. S. Rybakov and I. V. Mishustin,
"On the theory of a plane framework structure which is quasi-regular in
one direction," Mekh. Komposit. Mater. i Konstrukt., Vol. 2, No. 1,
pp. 41-50, 1996. |
| 4. | L. S. Rybakov and I. V. Mishustin,
"The theory of a plane framework structure which is quasi-regular in two
directions," Mekh. Komposit. Mater. i Konstrukt., Vol. 2, No. 3-4,
pp. 88-98, 1996. |
| 5. | L. Collatz, Eigenvalue Problems [Russian translation], Nauka, Moscow, 1968. |
|
| Received |
12 September 2000 |
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