连接结构局部状态改变所致波模态转换特性的数值分析方法

王文君; 范雨; 李琳

doi:10.13224/j.cnki.jasp.20220902

连接结构局部状态改变所致波模态转换特性的数值分析方法

doi: 10.13224/j.cnki.jasp.20220902

王文君¹,
范雨^{1, 2,*, ,},
李琳^{1, 2}

1.
北京航空航天大学能源与动力工程学院，北京 100191
2.
北京航空航天大学航空发动机结构强度北京市重点实验室，北京 100191

基金项目: 国家科技重大专项（2017-Ⅳ-0002-0039，J2019-Ⅳ-0023-0091）；航空科学基金（2019ZB051002）；先进航空动力创新工作站（HKCX2020-02-013，HKCX2020-02-016）

详细信息

作者简介:
王文君（1994-），男，博士，研究方向为结构健康监测

通讯作者:
范雨（1987-），男，副教授，博士，研究方向为振动控制、结构波传导、智能结构。E-mail：fanyu04@buaa.edu.cn

中图分类号: V19
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出版历程
- 收稿日期: 2022-11-23
- 网络出版日期: 2024-05-30

Numerical methods for analysis of wave conversion induced by local defects in structural joints

WANG Wenjun¹,
FAN Yu^{1, 2,*
, ,},
LI Lin^{1, 2}

1.
School of Energy and Power Engineering，Beihang University，Beijing 100191，China
2.
Beijing Key Laboratory of Aero-Engine Structure and Strength，Beihang University，Beijing 100191，China

摘要

摘要:
提出了一种数值方法来计算连接结构局部状态变化所致的波模态转换特性，并以柱壳-法兰为例，分析了不同局部状态下的波模态转换规律，结果发现不同局部状态变化会导致某些特征波模态发生剧烈的幅值变化。首先，改进了波有限元的Zhong-Williams格式，使其能够计算柱壳结构中的重根波模态。将这些重根波模态与周向均布4颗螺栓的法兰有限元模型结合，给出了构造扩散矩阵的主要步骤。其次，采用频散曲线和强迫响应验证了所提方法的数值精度。最后，线性降低螺柱弹性模量来表征螺栓某种局部状态变化，并依次向法兰连接入射周向波数为0～8的行波模态。结果发现单个螺栓、相邻螺栓、对角螺栓状态变化会将能量从入射波模态转入到某些特征波模态中，其幅值相对变化量最高可达36倍。这说明特征波模态之间的能量转换能够为连接结构的局部状态监测提供一种极具敏感性的指标。
- 波有限元法 /
- Zhong-Williams格式 /
- 螺栓松动 /
- 结构健康监测 /
- 波模态转换
Abstract:
A promising indicator was presented to identify connection states. A numerical method was proposed to compute the wave conversion induced by the local change of the connection joint. The cylinder with a flange was used as an example. The Zhong-Williams scheme was extended to resolve the repeated-root wave shapes by developing an iterative method based on the inverse power method. In combination with the finite element model of the flange joint, the general steps were introduced to construct a diffusion matrix. The dispersion curves and the forced responses were subsequently employed to verify the numerical accuracy of the proposed method and the diffusion matrix. Finally, propagating waves with a circumferent wavenumber of 0—8 were entered into the joint. The local changes allowed for reducing the elastic modulus of the bolts for simplicity. Results showed that the variations in a single bolt, adjacent bolts, and diagonal bolts can convert the energy from the incident waves to some propagating and evanescent waves. The amplitudes of the converted waves increased up to 36 times. It indicated that wave conversion is a promising indicator to monitor the local statuses of joint structures.
- wave finite element method /
- Zhong-Williams scheme /
- bolt looseness /
- structural health monitoring /
- wave-mode conversion

HTML

图 1 波导-连接（单位：m）

Figure 1. Waveguide-joint （unit：m）

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图 2 算法框架

Figure 2. Algorithm framework

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图 3 周期结构的第i个元胞

Figure 3. ith unit cell of periodic structure

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图 4 连接结构的波散射

Figure 4. Wave scattering introduced by joint structure

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图 5 柱壳结构的频散曲线

Figure 5. Dispersive curves of cylindrical shell structure

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图 6 波模态振型

Figure 6. Wave shapes

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图 7 强迫响应的有限元模型

Figure 7. Finite element model for forced response

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图 8 节点1的强迫响应

Figure 8. Forced response of node 1

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图 9 透射行波幅值

Figure 9. Amplitudes of propagating waves

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图 10 透射快衰波幅值

Figure 10. Amplitudes of evanescent waves

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图 11 单个螺栓不同连接状态下透射波的波幅值（入射波模态为L4）

Figure 11. Transmitted wave amplitudes of different operating conditions of single bolt （induced by incident wave L4）

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图 12 单个螺栓不同连接状态下的波幅值

Figure 12. Wave amplitudes of different operating conditions of single bolt

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图 13 相邻两个螺栓相同连接状态的波幅值

Figure 13. Wave amplitudes of the same operating conditions of two adjacent bolts

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图 14 对角两个螺栓相同连接状态的波幅值

Figure 14. Wave amplitudes of the same operating conditions of two diagonal bolts

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