 | | 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 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| L. D. Akulenko and S. V. Nesterov, "Vibrations of strings and beams in an inhomogeneous elastic medium," Mech. Solids. 41 (2), 47-53 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
2 |
Pages |
47-53 |
| Title |
Vibrations of strings and beams in an inhomogeneous elastic medium |
| Author(s) |
L. D. Akulenko (Moscow)
S. V. Nesterov (Moscow) |
| Abstract |
Vibrations of distributed systems in an inhomogeneous medium are
considered. The dependence of the eigenvalues (eigenfrequencies) of
the corresponding boundary-value problem with strongly varying
coefficients on the system parameters is studied for arbitrary
boundary conditions of elastic support. It is proven that the presence
of the Winkler term in the equation can lead to abnormal behavior,
i.e., to the increase in the lower natural vibration frequencies with
the growth of the interval length. Fine features of the variation of
the eigenfrequencies with the interval length and vibration mode
number unknown previously in the scientific literature have been
obtained. A numerical-analytical study is carried out for several
example problems demonstrating the characteristic behavior of the
solutions describing the natural vibrations of strings and beams in an
elastic medium. |
| References |
| 1. | L. D. Akulenko and S. V. Nesterov,
High-precision Methods in Eigenvalue Problems and their Applications,
CRC Press, Boca Raton, 2005. |
| 2. | R. Courant and D. Hilbert, Methods of Mathematical Physics. Volume 1,
Wiley, New York, 1989. |
| 3. | V. I. Smirnov, A Course in Higher Mathematics. Volume 4. Part 2 [in Russian],
Nauka, Moscow, 1981. |
| 4. | G. Korn and T. Korn, Mathematical Handbook for
Scientists and Engineers [Russian translation],
Nauka, Moscow, 1970. |
| 5. | L. D. Akulenko and S. V. Nesterov, "Determination of
frequencies and vibration modes of inhomogeneous
distributed systems with boundary conditions of the third kind,"
PMM [Applied Mathematics and Mechanics], Vol. 61, No. 4,
pp. 547-555, 1997. |
| 6. | L. D. Akulenko, "High-frequency natural vibrations of
mechanical systems,"
PMM [Applied Mathematics and Mechanics], Vol. 64, No. 5,
pp. 817-832, 2000. |
|
| Received |
07 September 2005 |
| << Previous article | Volume 41, Issue 2 / 2006 | Next article >> |
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