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工程力学 2014

基于梁理论的复杂梁式结构低阶频率快速求解方法

DOI: 10.6052/j.issn.1000-4750.2013.03.0174, PP. 1-8

李取浩,王文胜,程耿东

Keywords: 梁式结构,平截面假设,位移插值函数,降阶模型,Krylov子空间

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Abstract:

工程计算中常遇到纵向尺度显著大于横向的复杂梁式结构,基于此类大型复杂结构的精细有限元模型建立一个能够预测结构动力性能、实现复杂结构的快速动力分析和优化的近似降阶模型,成为这类结构设计工作者一直关心的问题。该文提出一种基于梁平截面假设和梁位移插值函数的动力模型降阶方法,建立了具有明确物理意义的降阶模型。利用降阶模型计算得到的模态向量是原结构特征向量的高精度近似,基于一次瑞利-里茨逆迭代获得了原结构高精度的低阶频率,并且与Krylov子空间法进行了对比。具体算例表明了降阶方法的有效性。

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