粘弹性圆柱壳在轴向恒压下的动力稳定性

THE DYNAMIC STABILITY OF VISCOELASTIC CYLINDRICAL SHELL UNDER AXIAL CONSTANT LOAD

基于Timoshenko-Mindlin假设,得到考虑粘弹性的各向同性圆柱壳及纤维增强正交铺设层合圆柱壳在轴向恒压下的动力学方程。文中对两端简支的圆柱壳进行了分析,依Laplace变换,导出动力稳定的特征方程,由Routh-Hurwitz判据建立动力稳定性条件,对两类圆柱壳讨论了横向剪切变形的影响。

The dynamic stability is studied for isotropic viscoelastic cylindrical shell and symmetrically cross-ply laminated viscoelastic cylindrical shell under constant axial loading. The basic equations are established based on Timoshenko-Mindlin theory, the characteristics equation are derived by Laplace transformation for those two kinds of cylindrical shells with two simply supported ends. The stability condition applied in the calculation of critical loads is determined through Routh-Hurwitz theorem. In the numerical examples, critical loads are reduced due to the relaxation feature of the materials and greater effects of transverse shearable deformation on the critical loads are observed in symmetrically cross-ply laminated viscoelastic cylindrical shell than in isotropic viscoelastic cylindrical shell. The influence of rotary inertia is rather small and can be ignored.