 | | 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, V. P. Radin, V. P. Chirkov, and A. V. Shchugorev, "Stability of a non-potentially loaded cantilever beam restrained by an elastic spring," Mech. Solids. 41 (2), 65-71 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
2 |
Pages |
65-71 |
| Title |
Stability of a non-potentially loaded cantilever beam restrained by an elastic spring |
| Author(s) |
V. V. Bolotin (Moscow)
V. P. Radin (Moscow)
V. P. Chirkov (Moscow)
A. V. Shchugorev (Moscow) |
| Abstract |
One of the characteristic features of mechanical systems loaded by
non-conservative positional (follower) forces is that under certain
conditions various instability types can occur [1, 2]. If all
solutions of the equations of motion are monotonic near the
instability boundary in the parameter space, the instability is
referred to as divergence. If some of the solutions are oscillatory,
the instability is referred to as flutter. For systems with lumped
parameters, a classical example of such a system is the Ziegler
pendulum [3], while an example for distributed elastic systems is a
cantilever beam loaded by the potential ("dead") and follower
forces [4]. When studying such systems, the main aim is to construct
the critical surface separating in the parameter space the stable
equilibrium region from the instability region. This critical
surface (the stability boundary) consists of different parts,
crossing of which corresponds to different instability modes. The
bifurcation types of non-conservative systems depend both on the
external loading parameters and on the internal parameters. In this
study, a systematic stability analysis is carried out for a beam
clamped at one end, restrained by an elastic spring at the other
end, and loaded by a potential and follower forces. The influence
of the elastic spring stiffness on the position of the critical
surface and on the instability type occurring upon crossing this
surface is analyzed. The stability boundary is constructed by two
methods, using the continuum mechanics approach, i.e., by solving
the boundary-value problem, or by means of the series expansion with
respect to the natural vibration modes (the method of normal
coordinates). For the Ziegler pendulum restrained by an elastic
spring, the divergence-type bifurcation problem has been considered
in [5]. |
| References |
| 1. | V. V. Bolotin, Dynamic Stability of Elastic Systems [in Russian],
Gostekhizdat, Moscow, 1956. |
| 2. | V. V. Bolotin, Non-conservative Problems of the Theory
of Elastic Stability [in Russian], Fizmatgiz, Moscow, 1961. |
| 3. | H. Ziegler, "Stabilitätatskriterien der Elasomechanik,"
Ing. Arch, Vol. 20, No. 1,
pp. 49-56, 1952. |
| 4. | V. V. Bolotin and N. I. Zhinzher, "Stability of linear systems,"
in: Mashinostroenie. Encyclopedia in 40 Volumes, Vols 1-3, pp. 462-472,
Mashinostroenie, Moscow, 1994. |
| 5. | I. G. Boruk, L. G. Lobas, and L. D. Patrizio, "On the
equilibrium states of a double pendulum
with a follower force at the elastically restrained upper end,"
Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 16-22, 2004. |
| 6. | A. A. Grishko, A. V. Petrovskii, and V. P. Radin,
"The effect of internal friction
on the stability of a panel in a supersonic gas flow," Izv. AN. MTT [Mechanics of Solids], No. 1,
pp. 173-181, 1998. |
| 7. | V. V. Bolotin (Editor), Vibrations in Engineering. Handbook. Volume 1 [in Russian],
Mashinostroenie, Moscow, 1999. |
|
| Received |
02 July 2005 |
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