轴压作用下粘弹性柱壳的动力学行为

基于大挠度薄壳的K?rm?n-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K?rm?n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。

Dynamical Behavior ofViscoelastic Cylindrical Shells Under Axial Pressures

The hypotheses of the Krmn-Donnell t heory of thin shells with large deflections and the Boltzmann laws for isotropic linear, viscoelastic materials, the constitutive equations of shallow shells ar e first derived. Then the governing equations for the deflection and stress func tion are formulated by using the procedure similar to establishing the Krmn equations of elastic thin plates. Introducing proper assumptions, an approximate theory for viscoelastic cylindrical shells under axial pressures can be obtaine d. Finally, the dynamical behavior is studied in detail by using several numeric al methods. Dynamical properties, such as, hyperchaos, chaos, strange attractor, limit cycle etc.,are discovered.