含裂纹缺陷的预扭壳结构非线性振动特性研究

Nonlinear vibration characteristic analysis of a cracked pre-twisted shell

基于扩展等几何方法和一阶壳体剪切变形理论建立了含裂纹缺陷的功能梯度预扭壳结构的非线性振动控制方程。控制方程中考虑了预扭壳结构的预扭角度及几何非线性,应用扩展等几何方法,采用反映位移变化的富集函数来描述裂纹的位置及长度,一方面可以提高计算精度,另一方面可以避免在裂纹处的网格加密,提高计算效率。采用了直接迭代法求解非线性振动控制方程。通过与现有文献结果对比,证明了本文方法的正确性和稳定性。在此基础上,探究裂纹对功能梯度预扭壳结构非线性振动频率的影响,研究了预扭角度、裂纹位置及长度和材料的功能梯度指数等参数对预扭壳非线性振动特性的影响规律。

This paper establishes the governing equations of the nonlinear vibration of a functionally graded shell with a crack,based on the extended isogeometric analysis(XIGA)and the first-order shear deformation theory.The study investigates the ef-fects of the crack on the nonlinear vibrational frequency ratio of the model,taking into account large amplitude vibrations.Enriched functions,which represent displacement changes,are used to describe the position and length of the crack.This approach enhances calculation accuracy and avoids mesh refinement at the crack.The nonlinear governing equation is solved using the direct iteration method,and its correctness is validated by comparing the results with existing literature.The study further explores the effects of the pre-twisted angle,crack location,crack length and material variation parameters on the nonlinear vibration characteristics of the pre-twisted shells with cracks.