多跨连续梁自由振动的动态有限元分析

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (15) : 150-159.

论文

多跨连续梁自由振动的动态有限元分析

夏桂云,刘明暕,温睿

作者信息 +

Dynamic finite element analysis for free vibration of multi-span continuous beams

XIA Guiyun, LIU Mingjian, WEN Rui

Author information +

文章历史 +

摘要

利用Timoshenko梁振动微分方程的奇次解，建立了单元任意截面的变形、内力与结点位移的关系，取端点截面的内力得到动态有限元列式。动态有限元具有不依赖网格密度、可准确计算任意阶次的振动频率和振型等特点。利用动态有限元刚度矩阵行列式为0条件，推导出1～4跨等截面等跨径的多跨连续梁频率方程。分析了多跨连续梁的自由振动，结果表明，相应简支梁的频率为多跨连续梁的固有频率、振型经扩展后为多跨连续梁的振型；多跨连续梁的振动有第二频谱现象和梁高振动特征。

Abstract

Using the homogeneous solutions to the differential motion equation of Timoshenko beams, deformations and inner forces are expressed by the nodal displacements at arbitrary cross-section. When the nodal forces are evaluated, the dynamic finite element will be formulated. Dynamic finite element formulation can achieve arbitrary-order frequencies and vibrating modes precisely, which does not depend on the mesh density. Incorporating the algorithm of the general stiffness matrix determinant being zero, frequency equations of multi-span continuous Timoshenko beam with 1~4 spans are derived. Free vibration analyses of multi-span continuous Timoshenko beam are conducted. Results demonstrate that the frequencies of the corresponding simply-supported Timoshenko beam are all natural frequencies of multi-span continuous Timoshenko beams. The vibrating modes of the corresponding simply-supported Timoshenko beam are extended to form the vibrating modes of multi-span continuous Timoshenko beams. Multi-span continuous Timoshenko beams possess the properties of the second frequency spectrum and beam height vibration.

导出引用

夏桂云,刘明暕,温睿. 多跨连续梁自由振动的动态有限元分析[J]. 振动与冲击, 2024, 43(15): 150-159

XIA Guiyun, LIU Mingjian, WEN Rui. Dynamic finite element analysis for free vibration of multi-span continuous beams[J]. Journal of Vibration and Shock, 2024, 43(15): 150-159

参考文献

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