空间细长杆-梁结构热致振动分析

doi:10.19665/j.issn1001-2400.2022.03.026

摘要/Abstract

摘要：

针对截面无温差柔性细长杆-梁结构在温度载荷下引发的热致振动机理不明问题,以“L”形直角梁为研究对象,建立了热致振动数学模型,并提出了等效轴力法。该方法基于有限元思想,将不同单元的节点温度变化等效为热轴力进行加载,并进行动力学分析,验证了即使杆-梁结构截面内不存在温差,只要温度变化可使结构发生变形且温度场快速动态变化,就会产生热振动现象,补充完善了“只有横截面内存在温度梯度,才会引起热致振动”理论,为研究复杂结构的热致振动响应提供了新的思路。随后在“L”形直角梁算例中,将提出的等效轴力法计算结果与等效位移法计算结果进行对比。结果表明:两种方法计算误差在0.002 2%内,但等效轴力法相比等效位移法时间减少了79%,验证了这种方法的正确性与高效性;空间杆件之间的相互作用会引起结构弯曲变形,在特定温度条件下,会发生热致振动。最后利用等效轴力法对环形可展开天线刚性支撑的周边桁架结构进行了热致振动数值分析。

关键词: 热致振动, 热冲击, 细长杆-梁, 截面无温差, 有限元分析

Abstract:

To solve the unknown problem of thermally induced vibration (TIV) of slender rod-beam structures without cross-section temperature gradients under temperature loads,the “L-shaped” right-angle beam is taken as the object,and the TIV mathematical model and the equivalent axial force method are proposed.Based on the finite element method,the nodes’ temperature changes of different elements are equivalent to the thermal axial force for loading,with dynamic analyses carried out.It is verified that TIV occurs as long as the temperature changes cause the structure to deform and that the temperature fields change rapidly,even if there are no cross-section temperature gradients.The theory of “only the temperature gradients in the cross-section can cause TIV” is improved,and this paper provides a new method for studying TIV of complex structures.Then in the “L-shaped” right-angle beam study,the results calculated by this method are compared with those by the equivalent displacement method,with the results indicating that their error is within 0.002 2%,but the time required by the equivalent axial force method is 79% less than that by the equivalent displacement method,which verifies the rationality and effectiveness of this method.What is more,the interaction between the rods can cause the structure to bend,which can lead to TIV under a certain temperature condition.Finally,TIV of the hoop-truss is analyzed based on the method in this paper.

Key words: thermally induced vibration, thermal shock, slender rod-beam structures, without cross-section temperature gradients, finite element analysis

中图分类号:

V414.33

冯雨晴,马小飞,王辉,范超,王晶. 空间细长杆-梁结构热致振动分析[J]. 西安电子科技大学学报, 2022, 49(3): 230-237.

FENG Yuqing,MA Xiaofei,WANG Hui,FAN Chao,WANG Jing. Analysis of thermally induced vibration of space slender rod-beam structures[J]. Journal of Xidian University, 2022, 49(3): 230-237.

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阶数	固有频率f/Hz	阶数	固有频率f/Hz
1	82.891	6	640.82
2	120.12	7	942.03
3	268.16	8	1 015.6
4	329.79	9	1 213.7
5	557.60	10	1 230.4

方法	x方向最大准静态位移	x方向最大动态位移	y方向最大准静态位移	y方向最大动态位移
等效位移法/m	6.635 74×10^-5	6.819 73×10^-5	-9.955 28×10^-5	-10.147×10^-5
等效轴力法/m	6.635 74×10^-5	6.819 87×10^-5	-9.955 28×10^-5	-10.1472×10^-5
误差/%	0	0.002 1	0	0.002 0