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力学学报  2015 

光滑节点插值法:计算固有频率下界值的新方法

DOI: 10.6052/0459-1879-15-146, PP. 839-847

Keywords: 柔性梁,光滑节点插值法,无网格法,动力学,固有频率下界

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Abstract:

将光滑节点插值法用于悬臂梁的静力学,并首次用于旋转柔性梁的频率分析.采用梯度光滑技术,用线性插值形函数描述梁的位移场,求解4阶微分方程.在静力学分析中,将该方法所得梁中各点位移与假设模态法、有限元法及解析解的结果对比,可知该方法虽用简单的线性插值形函数描述梁的位移场,但精度却很高.进一步研究表明,采用模态高于9阶的假设模态法会使刚度阵条件数变差,导致结果发散.在频率分析中,与有限元法、假设模态法和解析解对比,表明该方法一个重要特性能提供固有频率的下界值,而有限元法和假设模态法只能提供固有频率的上界值,说明该方法结合有限元法在处理无解析解的问题时可以从上下界最大程度的逼近真实解,提高精度.光滑节点插值法具有形函数结构简单、独立变量少且能提供固有频率下界值的特性,因此,具有较高的推广及应用价值.

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