 | | 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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| V. V. Bolotin, A. V. Petrovskii, and V. P. Radin, "Stability and postcritical behavior of a multilink system of rigid bodies subjected to nonpotential loading," Mech. Solids. 40 (1), 142-152 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
1 |
Pages |
142-152 |
| Title |
Stability and postcritical behavior of a multilink system of rigid bodies subjected to nonpotential loading |
| Author(s) |
V. V. Bolotin (Moscow)
A. V. Petrovskii (Moscow)
V. P. Radin (Moscow) |
| Abstract |
A multilink system of rigid bodies is considered, the links of which are loaded by dead
forces (inertia forces). The rear link is loaded by a follower force (thrust
force) directed along the axis of the lowest link. The links are connected to
each other by viscoelastic elements the characteristics of which are assumed to be
linear. The principal axes of these elements are orthogonal to each other. In
the unloaded state, the planes of these axes (principal planes) are orthogonal
to the axes of the links of the system and parallel to each other. In the
loaded state, the axes are turned relative to each other in the principal
planes. The stability of the trivial solution of the problem, for
which the deviation of the longitudinal axes of the links from the vector of
acceleration of the center of mass of the system is zero, is analyzed. The boundaries of the
divergence and flutter domains are constructed. The postcritical behavior of
the system is analyzed numerically. In particular, the dynamic behavior of the
system under slowly changing thrust force is analyzed. This analysis made it
possible to establish the types of dynamic behavior, find the bifurcations of
the modes, and determine the domains of chaotic behavior of the system.
The behavior of elastic systems subjected to nonpotential (in particular,
follower) forces has been studied fairly thoroughly [1-6]. However, quite a lot
of problems still remain, which are of interest from the standpoint of the
nonlinear dynamics. One of such problems is that of the dynamic behavior
of a system of rigid bodies (links) connected by viscoelastic elements and
loaded by dead and follower forces. An example of dead forces are the inertia
forces, provided that the direction of the vector of acceleration of the center
of mass is constant. A follower force is the thrust force. In this system, the
quasistatic (divergence) and dynamic (flutter) types of loss of stability
are possible. It is of interest to analyze the combination of these types. In
this case, the effect of secondary flutter is possible in the
divergence domain. This effect was first observed for aeroelastic systems [7] and then
thoroughly analyzed [8-10]. In the present study, the complete systematic
analysis of both the equilibrium states of divergence kind and the motions in
the flutter domain is performed for a system of three links. Major
attention is given to the analysis of stability of the direction of the
acceleration of the center of mass of the system. |
| References |
| 1. | V. V. Bolotin, "On the vibrations and stability of rods loaded by
nonconservative forces," in Vibrations in Turbomachines [in Russian], pp. 23-42, Izd-vo AN
SSSR, Moscow, 1959. |
| 2. | V. V. Bolotin, Nonconservative Problems of the Theory of Elastic
Stability [in Russian], Fizmatgiz, Moscow, 1961. |
| 3. | V. V. Bolotin nad N. I. Zhinzher, "Effects of damping on stability of
elastic systems subjected to nonconservative forces," Int. J. Solid Struct.,
Vol. 5, No. 9, pp. 965-989, 1969. |
| 4. | N. I. Zhinzher, "Influence of dissipative forces with incomplete
dissipation on the stability of elastic systems," Izv. AN. MTT [Mechanics of
Solid], No. 1, pp. 149-155, 1994. |
| 5. | J.-D. Jin, "Bifurcation analysis of double pendulum with a follower
force," J. Sound Vibr., Vol. 154, No. 2, pp. 191-204, 1992. |
| 6. | A. N. Kounadis, "On the failure of static stability analyses of
nonconservative systems in domains of divergence instability," Int. J. Solids
and Structures, Vol. 31, No. 15, pp. 2099-2120, 1994. |
| 7. | V. V. Bolotin, A. V. Petrovsky, and A. A. Grishko, "Secondary
bifurcations and global instability of an aeroelastic nonlinear system in the
divergence domain," J. Sound Vibr., Vol. 191, No. 3, pp. 431-451, 1996. |
| 8. | A. A. Grishko, A. V. Petrovskii, and V. P. Radin, "On the influence of
the internal friction on the stability of a panel in the supersonic gas flow,"
Izv. AN. MTT [Mechanics of Solid], No. 1, pp. 173-181, 1998. |
| 9. | V. V. Bolotin, A. A. Grishko, A. N. Kounadis, and Ch. Gantes,
"Non-linear panel flutter in remote post-critical domain," Int. J. Non-Linear
Mechanics, Vol. 33, No. 5, pp. 753-764, 1998. |
| 10. | V. V. Bolotin, A. A. Grishko, A. N. Kounadis, Ch. Gantes, and
J. B. Roberts, "Influence of initial conditions on the postcritical behavior
of nonlinear aeroelastic systems," J. Nonlinear Dynamics, No. 15, pp. 63-81,
1998. |
| 11. | A. V. Petrovskii, "Stability and postcritical bshavior of an
inverted three-dimensional pendulum subjected to nonpotential loading,"
Izv. AN. MTT [Mechanics of Solid], No. 1, pp. 165-176, 2002 |
| 12. | V. V. Bolotin (Editor), Vibrations in Engineering. Handbook. Volume 1.
Vibrations of Linear Systems [in Russian], Mashinostroenie, Moscow, 1999. |
| 13. | A. A. Grishko, Yu. A. Dubovskikh, and A. V. Petrovskii, "On the
postcritical behavior of nonlinear dissipative systems," Prikladnaya
Mekhanika, Vol. 34, No. 6, pp. 92-98, 1998. |
|
| Received |
27 April 2004 |
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