 | | 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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| V. V. Bolotin and A. A. Grishko, "Stability and post-critical behavior of aeroelastic systems with additional damping," Mech. Solids. 38 (5), 136-142 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
5 |
Pages |
136-142 |
| Title |
Stability and post-critical behavior of aeroelastic systems with additional damping |
| Author(s) |
V. V. Bolotin (Moscow)
A. A. Grishko (Moscow) |
| Abstract |
The influence of damping on the stability and post-critical behavior of time-invariant non-potential systems is considered by using an example of a thin elastic panel subjected to a supersonic gas flow. A method is developed for numerical simulation of steady-state vibrations of nonlinear systems after the stability boundary of the initial state has been intersected. Three types of damping, (i) aerodynamic damping, (ii) Voigt's internal friction in accordance to which the damping is more pronounced for higher modes, and (iii) structural damping that affects certain modes, as well as combinations of these, are considered. In some cases, secondary and higher-order bifurcations, as well as hysteresis in case the control parameters change non-monotonically, have been identified. Although the analysis has been performed for a specific mechanical model, the equations obtained after discretizing the primary equation are fairly general. The distribution of damping among the vibration modes is shown to substantially influence the post-critical behavior, the type of which can qualitatively change under certain conditions. |
| References |
| 1. | H. Ziegler, "Die Stabilizataetskriterien der Elastomechanik,"
Ing. Arch, Bd. 20, H. 1, pp. 49-56, 1952. |
| 2. | V. V. Bolotin, "Nonlinear flutter of plates and shells,"
Inzhenernyi Sbornik, Vol. 28, pp. 55-75, 1960. |
| 3. | V. V. Bolotin, Non-conservative Problems in the Theory of Elastic Stability [in Russian], Fizmatgiz, Moscow, 1961. |
| 4. | V. V. Bolotin, "Stabilization and destabilization effects in mechanics of deformable systems,"
Proc. 6th Canadian Congr. on Appl. Mech., pp. 1-10, Vancouver, 1979. |
| 5. | A. A. Movchan, "On the stability of a panel moving in a gas,"
PMM [Applied Mathematics and Mechanics], Vol. 21, No. 2, pp. 321-243,
1957. |
| 6. | V. V. Bolotin, A. A. Grishko, and A. V. Petrovskii,
"On the influence of damping forces on the post-critical behavior of essentially non-potential systems,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 158-167, 1995. |
| 7. | V. V. Bolotin, A. A. Grishko, A. N. Kounadis, and C. Ghantes,
"Nonlinear panel flutter in remote post-critical domains,"
Int. J. Non-linear Mech., Vol. 33, No. 5, pp. 753-764, 1998. |
| 8. | V. V. Bolotin, A. A. Grishko, A. N. Kounadis, C. Ghantes,
and J. B. Roberts,
"Influence of initial conditions on the postcritical behavior of nonlinear aeroelastic systems,"
Nonlinear Dynamics and Control, Vol. 15, No. 1, pp. 63-81, 1998. |
| 9. | E. H. Dowell, "Flutter of a buckled plate as an example of chaotic motion of a deterministic autonomous system,"
J. Sound and Vibration, Vol. 85, No. 3, pp. 333-344, 1982. |
| 10. | A. G. Gorshkov, V. I. Morozov, A. T. Ponomarev, and F. N. Shklyarchuk, Aeroelasticity of Structures [in Russian],
Nauka, Moscow, 2000. |
| 11. | V. V. Bolotin, A. A. Grishko, and T. V. Mitrichev,
"Stability of a thin panel with attached members in a supersonic gas flow," Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 3-10, 1999. |
| 12. | V. V. Bolotin, "Dynamic instabilities in mechanics of structures," Appl. Mech. Rev., Vol. 52, No. 1, pp. R1-R9, 1999. |
|
| Received |
10 January 2002 |
| << Previous article | Volume 38, Issue 5 / 2003 | Next article >> |
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