Some dynamical properties of a viscoelastic cylindrical shell. (English) Zbl 0942.74032
Summary: We discuss the dynamic stability of a viscoelastic circular cylindrical shell subject to an axial compressive force and a uniformly distributed radial compressive load. By using Laplace transform, we obtain stability conditions for viscoelastic shells under constant loads. Then the classical dynamic methods allow to study various dynamical properties of viscoelastic shells and to examine the effect of parameters on the stability.
MSC:
| 74H55 | Stability of dynamical problems in solid mechanics |
| 74K25 | Shells |
| 74D05 | Linear constitutive equations for materials with memory |
Keywords:
Lyapunov exponent; Lyapunov spectrum; cell mapping; sufficient condition for stability; dynamic stability; viscoelastic circular cylindrical shell; axial compressive force; uniformly distributed radial compressive load; Laplace transformReferences:
| [1] | Ladopoulos E G. Nonlinear integro-differential eduations used in orthotropic shallow spherical shell analysis [J].Mech Res Commun, 1991,18 (2–3): 111–119 · Zbl 0725.73043 · doi:10.1016/0093-6413(91)90038-X |
| [2] | Drozdov A. Stability of viscoelastic shell under periodic and stochastic loading [J].Mech Res Commun, 1993,20 (6): 481–486 · Zbl 0802.73031 · doi:10.1016/0093-6413(93)90007-B |
| [3] | Tylikowski A. Dynamic stability of viscoelastic shell under time-dependent membrane loads [J].Int J Mech Sci, 1989,31 (8): 591–597 · Zbl 0694.73020 · doi:10.1016/0020-7403(89)90066-0 |
| [4] | Yang Tingqing.Theory of Viscoelasticity [M]. Wuhan: Huazhong, Technology University Press, 1989 (in Chinese) · Zbl 0775.73056 |
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