基于模态应变能法功能梯度Euler-Bernoulli梁和Timoshenko梁模型对损伤识别的影响分析

玻璃钢/复合材料 ›› 2017, Vol. 0 ›› Issue (2): 38-43.

基于模态应变能法功能梯度Euler-Bernoulli梁和Timoshenko梁模型对损伤识别的影响分析

岳世燕^{1, 2}, 杨真真³, 谢峰¹, 黄立新^{1, 4*}

1.广西大学土木建筑工程学院,南宁530004;
2.成都理工大学工程技术学院,乐山641000;
3.许昌学院土木工程学院,许昌461000;
4.广西大学工程防灾与结构安全教育部重点实验室,南宁530004

收稿日期:2016-09-28 出版日期:2017-02-28 发布日期:2017-02-28
通讯作者: 黄立新(1964-),男,博士,教授,博导,主要从事复合材料结构与力学等方面的研究,gxuhuanglixin@163.com。
作者简介:岳世燕(1991-), 女,硕士,助教,主要从事工程结构与力学等方面的研究。
基金资助:
国家自然科学基金(11262002)

ANALYSIS ON THE EFFECT OF EULER-BERNOULLI BEAM MODEL AND TIMOSHENKO BEAM MODEL ON DAMAGE IDENTIFICATION BASED ON MODAL STRAIN ENERGY METHOD

YUE Shi-yan^1,2, YANG Zhen-zhen³, XIE Feng¹ , HUANG Li-xin^1,4*

1.School of Civil Engineering, Guangxi University, Nanning 530004, China;
2.The Engineering &
Technical College of Chengdu University of Technology, Leshan 614000, China;
3.School of Civil Engineering, Xuchang University, Xuchang 461000, China;
4.The Key Laboratory of Disaster Prevention and Structural Safety of the Education Ministry, Guangxi University, Nanning 530004, China

Received:2016-09-28 Online:2017-02-28 Published:2017-02-28

摘要/Abstract

摘要： 随着功能梯度梁的跨高比从小(厚梁)变到大(薄梁),梁的变形受到剪切变形的影响就会从大变到小。为了准确分析功能梯度梁的变形,跨高比小的厚梁采用Timoshenko梁模型,而跨高比大的薄梁采用Euler-Bernoulli梁模型。采用这两种梁模型进行功能梯度梁自由振动的有限元计算,分析单元刚度矩阵、质量矩阵和模态阵型等存在的差异。通过数值算例,研究了这两种梁模型的差异对模态应变能法的损伤识别指标的影响。对于厚梁,Timoshenko梁模型的损伤指标优于Euler-Bernoulli梁模型;对于很薄的梁(例如,l/h=25时的薄梁),Euler-Bernoulli梁模型的损伤指标优于Timoshenko梁模型。

关键词: 功能梯度材料, Euler-Bernoulli梁模型, Timoshenko梁模型, 模态应变能, 损伤识别

Abstract: With the change of span-depth ratio of functionally graded (FG) beam from small (thick beam) to large (thin beam), the effect of shear deformation on the beam deformation decrease. In order to analyze the deformation of the beam accurately, Timoshenko beam model is used for the thick beam with small span-depth ratio and Euler-Bernoulli beam model is used for thin beam large span-depth ratio. In this paper, free vibration is calculated based on the two beam models by a finite element method (FEM) to further analysis on the difference between element stiffness matrix, mass matrix and modal mode. Numerical examples are given to analyze the effect of those differences on the damage identification index. The damage indices of Timoshenko beam model are better than those of Euler-Bernoulli beam model in thick beam, while the damage indices of Euler-Bernoulli beam model are better than those of Timoshenko beam model in thin beam (for example l/h=25).

Key words: functionally graded material, Euler-Bernoulli beam model, Timoshenko beam model, modal strain energy, damage identification

中图分类号:

TB332

岳世燕, 杨真真, 谢峰, 黄立新. 基于模态应变能法功能梯度Euler-Bernoulli梁和Timoshenko梁模型对损伤识别的影响分析[J]. 玻璃钢/复合材料, 2017, 0(2): 38-43.

YUE Shi-yan, YANG Zhen-zhen, XIE Feng , HUANG Li-xin. ANALYSIS ON THE EFFECT OF EULER-BERNOULLI BEAM MODEL AND TIMOSHENKO BEAM MODEL ON DAMAGE IDENTIFICATION BASED ON MODAL STRAIN ENERGY METHOD[J]. Fiber Reinforced Plastics/Composites, 2017, 0(2): 38-43.

参考文献

[1] Birman V, Byrd LW. Modeling and Analysis of Functionally Graded Materials and Structures[J]. Applied Mechanics Reviews, 2007, 60: 195-216.
[2] Jha DK, Tarun Kant, Singh RK. A critical review of recent research on functionally graded plates[J]. Composite Structures, 2013, 96: 833-849.
[3] Liew KM, Lei ZX, Zhang LW. Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review[J]. Composite Structures, 2015, 120: 90-97.
[4] 曹志远. 功能梯度复合材料圆柱壳基本理论及长壳固有振动解[J]. 玻璃钢/复合材料, 2006(4): 3-6.
[5] 曹志远. 功能梯度壳体力学的一般理论[J]. 玻璃钢/ 复合材料, 2008(2): 7-11.
[6] 仲政, 吴林志, 陈伟球. 功能梯度材料与结构的若干力学问题研究进展[J]. 力学进展, 2010, 40(5): 528-540.
[7] 黄立新, 姚祺, 张晓磊, 等. 基于分层法的功能梯度材料有限元分析[J]. 玻璃钢/复合材料, 2013(2): 43-48.
[8] 黄立新, 杨真真, 张晓磊, 等. 基于ABAQUS 的功能梯度材料等参梯度有限元分析[J]. 玻璃钢/复合材料, 2014(2): 33-39.
[9] Cornwell PJ, Doebling SW, Farrar CR. Application of the strain energy damage detection method to plate-like structures[J]. Journal of Sound and Vibration, 1999, 224 (2): 359-374.
[10] Shi ZY, Law SS, Zhang LM. Structural damage localization from modal strain energy change[J]. Journal of Sound and Vibration, 1998, 218 (5): 825-844.
[11] Shi ZY, Law SS, Zhang LM. Structural damage detection from modal strain energy change[J]. Journal of Engineering Mechanics, 2000, 126(12): 1216-1223.
[12] Li YY. Hyper sensitivity of strain-based indicators for structural damage identification: A review[J]. Mechanical Systems and Signal Processing, 2010, 24: 653-664.
[13] Alvandia A, Cremona C. Assessment of vibration-based damage identification techniques[J]. Journal of Sound and Vibration, 2006, 292: 179-202.
[14] 黄立新, 杨真真, 赵文举. 基于模态应变能变化率法的Euler-Bernoulli功能梯度梁的损伤识别[J]. 玻璃钢/复合材料, 2015(8): 14-17.
[15] 杨真真. Euler-Bernoulli功能梯度梁结构损伤识别的模态应变能法[D]. 南宁: 广西大学硕士学位论文, 2014.
[16] 黄立新,岳世燕,胡中明,等. 功能梯度经典梁损伤识别模态应变能变化率法的抗噪音性能研究[J]. 玻璃钢/复合材料, 2016(2): 35-39.
[17] Alshorbagy AE, Eltaher MA, Mahmoud FF. Free vibration characteristics of a functionally graded beam by finite element method[J]. Applied Mathematical Modelling, 2011, 35: 412-425.
[18] Simsek M. Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories [J]. Nuclear Engineering and Design, 2010, 240(4):697-705.