内应力对结构模态影响理论及数值验证

摘要

Proceeding from physical equation with internal stress ,the influence of initial stress on stiff-ness of structure was developed by FEM method and principal virtual work ;further ,the influence amplitude of internal stress on dynamical performance of structure was established by matrix norm a l-gorithm .The developed work was verified visually by structure example of two -node link and veri-fied numerically by example of ship hull structure with welding residual stress regarded as internal stress .T he research result indicates that the influence of initial stress on the behavior of vibration and could not be ignored if accuracy of vibration control of hull structure is deemed necessary .%采用有限元法，从具有内应力的单元物理方程出发，推导出内应力对刚度产生影响，进而建立了内应力对结构模态影响程度的表达式。以二节点杆件为例，通过对比有无内应力情况下刚度矩阵，证实内应力不仅影响结构刚度，进而使结构振动固有频率发生偏离。而且，还会滋生出新的振动模态，验证了内应力影响模态理论的准确性；以焊缝的残余应力作为内应力实例，船体舱段为结构实例，比较不同焊接残余应力水平下结构二阶垂向振动的频率，数值验证了内应力对结构模态的影响。