黄立新, 杨绍钊, 梁福安,等.基于模态应变能与频率融合方法的功能梯度铁木辛柯梁损伤识别研究[J].河南理工大学学报（自然科学版）,2023,42(1):168-174.

HUANG L X, YANG S Z, LIANG F A,et al.Study on damage identification of functionally graded Timoshenko beam based on the fusion of modal strain and frequency[J].Journal of Henan Polytechnic University(Natural Science) ,2023,42(1):168-174.

基于模态应变能与频率融合方法的功能梯度铁木辛柯梁损伤识别研究

黄立新1,2, 杨绍钊1, 梁福安1, 黄君1

1.广西大学 土木建筑工程学院，广西 南宁 530004；2.广西大学 工程防灾与结构安全教育部重点实验室，广西 南宁 530004

摘要:基于模态应变能和固有频率融合，提出识别功能梯度铁木辛柯梁损伤的新方法。由功能梯度铁木辛柯梁理论给出有限元计算公式，在此基础上计算得出梁结构的固有频率和阵型模态参数。由模态应变能与固有频率融合构造模态频率应变能的计算公式。基于模态频率应变能变化率，定义功能梯度铁木辛柯梁的损伤识别指标。数值算例表明，模态应变能和固有频率融合的损伤识别方法能够有效识别出结构的损伤单元，并且具有较好的抗噪声性能。

关键词:功能梯度铁木辛柯梁;模态频率应变能;损伤识别;有限元法

doi:10.16186/j.cnki.1673-9787.2021010122

基金项目:国家自然科学基金资助项目（11262002）

收稿日期:2021/01/25

修回日期:2021/05/17

出版日期:2023/01/25

Study on damage identification of functionally graded Timoshenko beam based on the fusion of modal strain and frequency

HUANG Lixin1,2, YANG Shaozhao1, LIANG Fuan1, HUANG Jun1

1.School of Civil Engineering and Architecture，Guangxi University，Nanning 530004，Guangxi，China；2.The Key Laboratory of Disaster Prevention and Structural Safety of the Education Ministry，Guangxi University，Nanning 530004，Guangxi，China

Abstract:Based on the fusion of modal strain energy and natural frequency，a new damage identification method of functionally graded（FG）Timoshenko beam was proposed in this paper.The finite element calculation scheme was given by way of the theory of FG Timoshenko beam and on this basis the natural frequency and shape modal parameters were calculated.The formula of the modal frequency strain energy was constructed after modal strain energy fusing with natural frequency.Based on the change rate of elemental modal frequency strain energy，the damage identification index of FG Timoshenko beam was defined.Numerical examples indicated that the damage identification method fusing modal strain energy with natural frequency could effectively identify damage elements and had good anti-noise performance.

Key words:functionally graded Timoshenko beam;modal frequency strain energy;damage identification;finite element method

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