﻿ 基于损伤柔度曲率的塔式起重机塔身结构损伤识别研究
 上海理工大学学报  2022, Vol. 44 Issue (6): 562-567 PDF

Damage identification of tower crane structure based on flexibility curvature
ZHOU Kui, LIU Yiran, XU Chenguang
School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: Tower cranes belong to the high-risk special equipment due to their own structural characteristics and the attributes of high-altitude operation, and they are prone to heavy casualties. When tower cranes have minor damage, timely detection and maintenance are the basis and premise to avoid the risk of accidents. Based on the engineering background of QTZ100 tower crane on a new project site of a university in Shanghai, the damage compliance curvature was taken as the damage index. The finite element calculation model was built to analyze the variation of structural stress and modal parameters under various minor damage conditions, and compared with the analysis results using the change rate of vibration mode as the damage index. Results show that the damage compliance curvature curve produces obvious mutation at the damage point, through which the location and degree of minor damage can be identified with good anti-noise performance.
Key words: tower crane     damage detection     flexibility curvature     numerical simulation

1 损伤识别方法 1.1 振型变化率

 $\Delta {\phi _i} = \phi _i^* - {\phi _i}$ (1)

 $\Delta \phi _i^* = \frac{{\Delta {\phi _i}}}{{{\phi _i}}} \times 100\text{%}$ (2)
1.2 损伤柔度曲率

a. 对获取的结构柔度矩阵F进行前后不等距的二阶中心差分，得到损伤柔度曲率矩阵C，其元素Cij

 $C_{ij} = \frac{{\left\{ {2{l_{\left( {i + 1} \right)i}}\left[ {{F_{\left( {i + 1} \right)j}} - {F_{ij}}} \right] - 2{l_{\left( {i - 1} \right)i}}\left[ {{F_{ij}} - {F_{\left( {i - 1} \right)j}}} \right]} \right\}}}{{\left[ {{l_{\left( {i + 1} \right)i}}{l_{i\left( {i - 1} \right)}}{l_{\left( {i + 1} \right)\left( {i - 1} \right)}}} \right]}}$ (3)

b. 将损伤柔度曲率矩阵C减去其转置矩阵CT的绝对值，得到了新的矩阵，记为相对损伤柔度曲率矩阵 ${{\boldsymbol{\omega}} _{{\rm{FCR}}}}$

 ${{\boldsymbol{\omega}} _{{\rm{FCR}}}} = \left| {{\boldsymbol{C}} - {\boldsymbol{C}}{^{\text{T}}}} \right|$ (4)

c. ${{\boldsymbol{\omega}} _{{\rm{FCR}}}}$ 按行均值计算得到相对损伤柔度曲率 ${\varepsilon _{{\rm{AFCR}}}}$

 ${\varepsilon _{{\rm{AFCR}}}}\left( i \right) = \frac{1}{N}\sum\limits_{j = 1}^N {{\omega _{{\rm{FC}}{{\rm{R}}_j}}}\left( i \right)}$ (5)

1.3 噪声模拟

 ${\omega '_i} = {\omega _i}\left[ {1 + \eta\; {\text{rand}}\left( { - 1,1} \right)} \right]$ (6)
 ${\phi'_i} = {\phi_i}\left[ {1 + \beta {\text{rand}}\left( { - 1,1} \right)} \right] + \gamma\; {\text{rms}}\left( {{f_i}} \right){\text{rand}}\left( { - 1,1} \right)$ (7)

2 数值模拟 2.1 有限元模型建立

2.2 损伤工况设计

 图 1 各节点位置示意图 Fig. 1 Schematic diagram of each node position

2.3 模拟研究

 图 2 振型变化率曲线 Fig. 2 Curve for the change rate of vibration mode

2.3.1 单处损伤

 图 3 单处不同程度损伤无噪和含噪下的振型变化率曲线和损伤柔度曲率矩阵曲线 Fig. 3 Curves for the change rate of vibration mode and the damage flexibility curvature matrix of a single point under different degrees of damage with and without noise

2.3.2 多处损伤

 图 4 多处不同程度损伤无噪和含噪下的振型变化率曲线和损伤柔度曲率矩阵曲线 Fig. 4 Curves for the change rate of vibration mode and the damage flexibility curvature matrix of multiple points under different degrees of damage with and without noise

2.3.3 螺栓损伤

 图 5 螺栓损伤的振型变化率曲线和损伤柔度曲率矩阵曲线 Fig. 5 Curves for the change rate of vibration mode and damage flexibility curvature matrix of bolt damage

3 结　论

a. 塔式起重机因其本身结构及工作环境的复杂性，极易发生事故。在其发生微小损伤时就及时发现并检修对规避事故风险非常重要。有限元仿真为塔机损伤检测提供了一种新方法。

b. 相对损伤柔度曲率矩阵仅需要结构损伤后的柔度矩阵，弥补了振型变化率的不足。

c. 基于振型变化率的损伤识别方法在多处损伤及噪声干扰下的识别效果较差。由柔度曲率矩阵构建出相对柔度曲率矩阵曲线可以有效识别单处损伤、多处损伤和螺栓损伤。并且能判定损伤程度。

d. 在随机噪声的影响下，基于损伤柔度曲率矩阵的方法基本不受随机噪声的干扰，抗噪性较优。

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