Dynamical Behavior of Viscoelastic Cylindrical Shells Under Axial Pressures

CHENG Chang-jun; ZHANG Neng-hui

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(1): 1-8

CHENG Chang-jun, ZHANG Neng-hui. Dynamical Behavior of Viscoelastic Cylindrical Shells Under Axial Pressures[J]. Applied Mathematics and Mechanics, 2001, 22(1): 1-8.

Citation:

CHENG Chang-jun, ZHANG Neng-hui. Dynamical Behavior of Viscoelastic Cylindrical Shells Under Axial Pressures[J]. Applied Mathematics and Mechanics, 2001, 22(1): 1-8.

Citation:

CHENG Chang-jun, ZHANG Neng-hui. Dynamical Behavior of Viscoelastic Cylindrical Shells Under Axial Pressures[J]. Applied Mathematics and Mechanics, 2001, 22(1): 1-8.

PDF( 348 KB)

Dynamical Behavior of Viscoelastic Cylindrical Shells Under Axial Pressures

Shanghai Institute of Applied Mathematics and Mechanics;Department of Mechanics, Shanghai University, Shanghai 200072, P R China

Received Date: 2000-03-21
Rev Recd Date: 2000-08-29
Publish Date: 2001-01-15

Abstract

Abstract

The hypotheses of the Kûrmûn-Donnell theory of thin shells with large deflections and the Boltzmann laws for isotropic linear,viscoelastic materials,the constitutive equations of shallow shells are first derived.Then the governing equations for the deflection and stress function are formulated by using the procedure similar to establishing the Kûrmûn equations of elastic thin plates.Introducing proper assumptions,an approximate theory for viscoelastic cylindrical shells under axial pressures can be obtained.Finally,the dynamical behavior is studied in detail by using several numerical methods. Dynamical properties,such as,hyperchaos,chaos,strange attractor,limit cycle etc.,are discovered.
- Kûrmûn-Donnell theory,
- viscoelastic cylindrical shell,
- chaos,
- hyperchaos,
- strange attractor,
- limit cycle

FullText(HTML)

References(12)

References

[1]	Potapov V D. Stability of compressed viscolelastic orthotropic shells[J]. J Appl Mech and Tech Phy,1978,18(4):586-592.
[2]	Minakova N I, Timakov V N. Axisymmetric stability of piecewise homogeneous viscoelastic shell acted on by the time-dependent uniform external pres sure[J]. Mech Solids,1978,13(1):134-138.
[3]	Drozdov A D. Stability of viscoelastic shells under periodic and stochastic loading[J]. Mech Res Commun,1993,20(6):481-486.
[4]	Brotskaya V Y, Milanovich O A, Minakova N I. Mathematical modeling of stability of a visco elastic shell with nonequal curvatures[J]. Mech Solids,1995,30(4):139-145.
[5]	DING Rui. The dynamical analysis of viscoelastic structures[D]. Ph D Thesis. Lanzhou: Lanzhou University,1997.
[6]	程昌钧,朱正佑. 结构的屈曲与分叉[M]. 兰州:兰州大学出版社,1991.
[7]	CHENG Chang-jun, ZHANG Neng-hui. Variational principles on static-dynamic analysis of viscoelastic thin plates with applications[J]. Int J Solids Struct,1998,35(33):4491-4505.
[8]	ZHANG Neng-hui, CHENG Chang-jun. Non-linear mathematical model of viscoelastic thin plates with its applications[J]. Comput Methods Appl Mech Engng,1998,165(4):307-319.
[9]	程昌钧,张能辉. 粘弹性矩形板的混沌和超混沌[J]. 力学学报,1998, 30(6):690-699.
[10]	徐芝纶. 弹性理论[M]. 北京:高等教育出版社,1988.
[11]	Shimada I, Nagashima T. A numerical approach to ergodic problem of dissipative systems[J]. Prog Theor Phys,1979,61(12):1605-1615.
[12]	Kubicek M, Marek M. Computational Methods in Bifurcation Theory and Dissipative Structures[M]. New York: Springer-Verlag,1983.