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An optimal form of the finite element mass matrix in the analysis of longitudinal vibrations of rods
Finite Elements in Analysis and Design ( IF 3.1 ) Pub Date : 2022-05-04 , DOI: 10.1016/j.finel.2022.103763
Marek Krawczuk , Magdalena Palacz

In this paper, an attempt is made to find the optimal form of the mass matrix of a rod finite element, which allows one to obtain the smallest errors in the longitudinal frequency determination of natural vibrations of any boundary conditions within the whole range of determined frequencies. It is assumed that the mass matrix can be treated as a linear combination of the consistent and diagonal matrices. Based on analytical considerations, the optimal values of certain weights for creating a linear combination of the mentioned matrices have been determined. As a result, a mass matrix has been obtained which allows the determination of natural frequencies with the smallest mean error within the possible spectrum of frequencies. It is also shown that the value of the weight coefficient changes depending on the number of natural frequencies within the spectrum one wants to determine.



中文翻译:

杆件纵向振动分析中有限元质量矩阵的一种优化形式

本文试图寻找杆有限元质量矩阵的最优形式,使得在整个确定频率范围内任意边界条件的固有振动的纵向频率确定中获得最小的误差。 . 假设质量矩阵可以被视为一致矩阵和对角矩阵的线性组合。基于分析考虑,已经确定了用于创建上述矩阵的线性组合的某些权重的最佳值。结果,获得了一个质量矩阵,它允许在可能的频谱范围内确定具有最小平均误差的自然频率。

更新日期:2022-05-04
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