 | | 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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| A. V. Petrovskii, "Dynamic behavior of an inverted non-orthogonal double pendulum subjected to a non-potential loading," Mech. Solids. 38 (5), 113-121 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
5 |
Pages |
113-121 |
| Title |
Dynamic behavior of an inverted non-orthogonal double pendulum subjected to a non-potential loading |
| Author(s) |
A. V. Petrovskii (Moscow) |
| Abstract |
The motion of an inverted non-orthogonal double pendulum the links of which are connected by means of a two-degree-of-freedom viscoelastic joint (gimbals) is studied in the cases where the pendulum is loaded by a dead force and a follower force. The boundaries of the primary stability regions (corresponding to the stability of the trivial equilibrium mode) are obtained. The boundaries of the region of existence of stable equilibriums in the divergence domain are found. The stability analysis is performed for the equilibrium states, depending on the character of the control force (the dead force or the follower force). The postcritical behavior of the pendulum is studied for near and remote postcritical domains.
The behavior of elastic systems under the action of non-conservative forces (in particular, follower forces) has been already thoroughly studied [1-6]. However, there are still many problems in these field that are of interest from the viewpoint of nonlinear dynamics. In this respect, rather interesting and indicative is the behavior of an inverted spatial double pendulum loaded by a dead force and a follower force. It is of interest to investigate the combination of quasi-static (divergence) and dynamic (flutter) types of instability. In this system one can observe the secondary flutter and the global instability in the divergence region. These phenomena were first discovered in [7] for aeroelastic systems and then were thoroughly studied in [8, 9].
The behavior of the inverted orthogonal double pendulum, of which links the principal planes of rigidity and inertia coincide, was studied in [5]. In the present paper, we investigate a non-orthogonal pendulum of which the principal planes of the upper link are turned by an appropriate angle with respect to the planes of the lower link. The links are connected to each other and to the base by means of linear viscoelastic two-degree-of-freedom joints (gimbals). We perform a complete systematic analysis of divergent-type equilibriums and the motion in the flutter domain. The basic method of the investigation (except for the primary stability analysis) is the computational experiment. |
| References |
| 1. | V. V. Bolotin, "On vibrations and stability of rods subjected to non-conservative forces,"
in Vibrations in Turbine Machines [in Russian], pp. 23-42,
Izd-vo AN SSSR, Moscow, 1959. |
| 2. | V. V. Bolotin, Non-conservative Problems in the Theory of Elastic Stability [in Russian], Fizmatgiz, Moscow, 1961. |
| 3. | V. V. Bolotin and N. I. Zhinzher,
"Effects of damping on stability of elastic systems subjected to nonconservative forces,"
Intern. J. Solid and Structures, Vol. 5, No. 9, pp. 965-989, 1969. |
| 4. | N. I. Zhinzher, "The influence of dissipative forces with incomplete dissipation on the stability of elastic systems,"
Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 149-155, 1994. |
| 5. | A. V. Petrovskii, "Stability and postcritical behavior of an inverted spatial pendulum subjected to nonpotential loading,"
Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 165-176, 2002. |
| 6. | J.-D. Jin and Y. Matsuzaki, "Bifurcation analysis of double pendulum with a follower force,"
J. Sound and Vibrat., Vol. 154, No. 2, pp. 191-204, 1992. |
| 7. | V. V. Bolotin, A. V. Petrovskii, and A. A. Grishko,
"Secondary bifurcations and global instability of an aeroelastic nonlinear system in the divergence domain,"
J. Sound and Vibrat., Vol. 191, No. 3, pp. 431-451, 1996. |
| 8. | 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. |
| 9. | A. A. Grishko, Yu. A. Dubovskikh, and A. V. Petrovskii,
"On the postcritical behavior of dissipative nonlinear systems,"
Prikladnaya Mekhanika, Vol. 34, No. 6, pp. 92-98, 1998. |
| 10. | Kim Sang-Yoon and Bambi Hu, "Critical behavior
of period doublings in coupled inverted pendulums,"
Phys. Rev. E, Vol. 58, No. 6a, pp. 7231-7242, 1998. |
| 10. | Kim Sang-Yoon and Bambi Hu, "Bifurcations and transitions to chaos in an inverted pendulum,"
Phys. Rev. E, Vol. 58, No. 3a, pp. 3028-3035, 1998. |
|
| Received |
26 March 2001 |
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