本文讨论矩阵奇异值分解技术在任意边界条件下圆柱壳自由振动中的应用。对于任意边界条件，圆柱壳的精确解过程会遇到求解8阶矩阵行列式的问题。本文采用奇异值分解技术，把行列式求解转换为奇异值求解，并且依据最小奇异值的零点获得圆柱壳的振动频率。本文结合圆柱壳的频散图，讨论了各种边界条件下自由振动频散-波数对在图中的对应点。数值算例表明，奇异值分解为任意边界下圆柱壳的自由振动提供一种新的方法。并对常用近似边界处理方法的精度进行探讨。
Circular cylindrical shells are used in many industrial cases, such as ship, cars, and aircrafts and so on. Many contributions could be found for free vibration analysis of circular cylindrical shells. The boundary conditions of shell are more complicated than those of beams or plates. There are two ways for solving free vibrations of circular cylindrical shells under arbitrary boundary conditions, exact and approximate methods. A singular value decomposition approach is provided for finding the free vibration frequencies. During frequency sweep procedure, the frequency which corresponding that minimum singular value is the natural frequency of shells. A numerical example is illustrated in present study. The results are compared with other classical approaches and experiments. The accuracy of singular value decomposition is also examined.
2016,(s1): 44-50 收稿日期：2016-07-19
DOI：10.3404/j.issn.1672-7619.2016.S1.007
分类号：U663.1
作者简介：汪志强(1990-),男,硕士研究生,主要从事潜艇结构振动和优化研究。
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