基于广义混合元的加筋圆柱壳振动特性分析

Vibration Analysis of Stiffened Cylindrical Shells Based on Generalized Mixed Element Method

采用有限元位移法分析加筋圆柱壳的自由振动特性问题是主流的方法,但大量试验和数值实例表明:位移元模型会导致模拟刚度偏硬,从而使得结构固有频率结果不够精确。针对这一现象提出了柱坐标系下的广义混合变分原理,并建立了相应的非协调广义混合元的无阻尼自由振动方程。通过合理地调节参数,使得非协调广义混合元的刚度矩阵比非协调位移元的刚度矩阵柔和。实例分析表明,在有限元网格模型一致的情况下,结构的固有频率结果更加准确。

Finite element displacement methods are the mainstream methods to analyze the free vibration characteristics of stiffened cylindrical shells,but a large number of experiments and numerical examples show that the displacement element model will lead to the rigidity of the simulation,which makes the natural frequency of the structure inaccurate.In view of this phenomenon,the generalized mixed variational principle in cylindrical coordinate system is proposed,and the corresponding undamped free vibration equation of nonconforming generalized mixed element is established.By adjusting the parameters reasonably,the stiffness matrix of the nonconforming generalized mixed element is softer than that of the nonconforming displacement element.The example analysis shows that the natural frequency of structure is more accurate when the finite element mesh model is consistent.