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**Dynamical response of hyper-elastic cylindrical shells under periodic load.**
*(English)*
Zbl 1235.74147

Summary: Dynamical responses, such as motion and destruction of hyper-elastic cylindrical shells subject to periodic or suddenly applied constant load on the inner surface, are studied within the framework of finite elasto-dynamics. By numerical computation and dynamic qualitative analysis of a nonlinear differential equation, it is shown that there exists a certain critical value for the internal load describing the motion of the inner surface of the shell. Motion of the shell is a nonlinear periodic or quasi-periodic oscillation when the average load of the periodic load or the constant load is less than its critical value. However, the shell will be destroyed when the load exceeds the critical value. The solution to the static equilibrium problem is a fixed point for the dynamical response of the corresponding system under a suddenly applied constant load. The property of fixed point is related to the property of dynamical solution and the motion of the shell. The effects of the thickness and load parameters on the critical value and on the oscillation of the shell are discussed.

### MSC:

74H55 | Stability of dynamical problems in solid mechanics |

74K25 | Shells |

74B20 | Nonlinear elasticity |

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\textit{J. Ren}, Appl. Math. Mech., Engl. Ed. 29, No. 10, 1319--1327 (2008; Zbl 1235.74147)

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