A study of chaotic motion in elastic cylindrical shells. (English) Zbl 0942.74036
Summary: We study the chaotic motion of an elastic cylindrical shell, the dynamic equation of which contains square and cubic nonlinear terms. By means of the Galerkin approach and the Melnikov method, the critical condition for chaotic motion has been obtained. Two demonstrative examples are discussed through Poincaré mapping, phase portrait and time history.
MSC:
| 74H65 | Chaotic behavior of solutions to dynamical problems in solid mechanics |
| 74K25 | Shells |
| 37N15 | Dynamical systems in solid mechanics |
Keywords:
square term; cubic term; single mode model; chaotic motion; elastic cylindrical shell; Galerkin approach; Melnikov method; Poincaré mapping; phase portrait; time historyReferences:
| [1] | Lee, J. Y.; Symonds, P. S., Extended energy approach to chaotic elastic-plastic response to impulsive loading, Int. J. Mech. Sci., 34, 139-157 (1992) |
| [2] | Moon, F. C.; Shaw, S. W., Chaotic vibration of a beam with nonlinear boundary conditions, Non-linear Mech., 18, 230-240 (1983) |
| [3] | Baran, P. D., Mathematical models used in studying the chaotic vibration of buckled beam, Mech. Res. Communi., 21, 189-196 (1994) · Zbl 0819.73048 |
| [4] | Holms, P.; Marsden, J., A Partial differential equation with infinitely many periodic orbits: chaotic oscillation of a forced beam, Arch. Ration. Mech. An., 76, 135-165 (1981) · Zbl 0507.58031 |
| [5] | Keragiozov, V.; Keoagiozova, D., Chaotic phenomena in the dynamic buckling of an elastic-plastic column under an impact, Nonlinear Dyn., 13, 1-16 (1995) |
| [6] | Han, Q., The dynamic buckling bifurcation and chaotic motion of several structures, (Doctor’s thesis (1996), Taiyuan Univ. Technol: Taiyuan Univ. Technol People’s Republic of China) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
