Dynamical Behavior of Viscoelastic Cylindrical Shells Under Axial Pressures
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摘要: 基于大挠度薄壳的Kûrmûn-Donnell理论和各向同性线粘弹性材料的Boltzmann定律,首先推导了浅壳的本构方程,然后利用与建立弹性薄板Kûrmûn方程类似的过程,得到了关于挠度和应力函数的控制方程。在合适的假设下,一种近似理论被用来分析轴压作用下粘弹性柱壳的力学行为。最后,利用各种数值方法考察了粘弹性柱壳的动力学行为,发现了超混沌、混沌、奇怪吸引子和极限环等多种动力学性质。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.
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Key words:
- Kûrmûn-Donnell theory /
- viscoelastic cylindrical shell /
- chaos /
- hyperchaos /
- strange attractor /
- limit cycle
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