DAMAGE IDENTIFICATION OF EULER-BERNOULLI FUNCTIONALLY GRADED BEAM BY THE MODAL STRAIN ENERGY CHANGE RATIO METHOD

Abstract

Abstract: A damage identification method based on modal strain energy is presented for an Euler-Bernoulli functionally graded beam. The finite element method is employed to compute the elemental stiffness matrix and the modal parameters such as mode shapes of the beam. The elemental modal strain energy, which is defined as the product of the elemental stiffness matrix and the second power of the mode shape component, is calculated by using the finite element method results. On this basis, the damage indicator for the Euler-Bernoulli functionally graded beam is developed by way of the change of the modal strain energy in each element before and after the occurrence of damage. A numerical example is given to illustrate the validity of the proposed method for the damage identification of the Euler-Bernoulli functionally graded beam. Numerical results show that the damaged element can be easily identified by using the damage indicator.

Key words: Euler-Bernoulli functionally graded beam, modal strain energy, damage identification, finite element method

CLC Number:

TB332

HUANG Li-xin, YANG Zhen-zhen, ZHAO Wen-ju. DAMAGE IDENTIFICATION OF EULER-BERNOULLI FUNCTIONALLY GRADED BEAM BY THE MODAL STRAIN ENERGY CHANGE RATIO METHOD[J]. COMPOSITES SCIENCE AND ENGINEERING, 2015, 0(8): 14-17.

References

[1] Birman V, Byrd LW. Modeling and Analysis of Functionally Graded Materials and Structures. Applied Mechanics Reviews, 2007, 60: 195-216.
[2] Jha DK, Tarun Kant, Singh RK. A critical review of recent research on functionally graded plates. Composite Structures, 2013, 96: 833-849.
[3] Liew KM, Lei ZX, Zhang LW. Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review. 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. 玻璃钢/复合材料, 2006, 189(4): 3-6.
[5] 曹志远. 功能梯度壳体力学的一般理论. 玻璃钢/复合材料, 2008, 199(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. 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. 玻璃钢/复合材料, 2013, 230(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. 玻璃钢/复合材料, 2014, 239(2): 33-39.
[9] Araújo dos Santos JV, Mota Soares CM, Mota Soares CA, et al. Development of a numerical model for the damage identification on composite plate structures. Composite Structures, 2000, 48: 59-65.
[10] Doebling SW, Farrar CR, Prime MB, et al. Technical Report LA-13070-MS. New Mexico, USA: Los Alamos National Laboratory, Los Alamos, 1996.
[11] Yam LH, Leung TP, Li DB, et al. Theoretical and experimental study of modal strain analysis. Journal of Sound and Vibration, 1996, 191 (2): 251-260.
[12] Ndambi JM, Vantomme J, Harri K. Damage assessment in reinforced concrete beams using eigenfrequencies and mode shape derivatives. Engineering Structures, 2002, 24: 501-515.
[13] Cornwell PJ, Doebling SW, Farrar CR. Application of the strain energy damage detection method to plate-like structures. Journal of Sound and Vibration, 1999, 224 (2): 359-374.
[14] Shi ZY, Law SS, Zhang LM. Structural damage localization from modal strain energy change. Journal of Sound and Vibration, 1998, 218 (5): 825-844.
[15] Shi ZY, Law SS, Zhang LM. Structural damage detection from modal strain energy change. Journal of Engineering Mechanics, 2000, 126(12): 1216-1223.
[16] Li YY. Hyper sensitivity of strain-based indicators for structural damage identification: A review. Mechanical Systems and Signal Processing, 2010, 24: 653-664.
[17] Alvandia A, Cremona C. Assessment of vibration-based damage identification techniques. Journal of Sound and Vibration, 2006, 292: 179-202.
[18] Simsek M, Kocaturk T. Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load. Composite Structures, 2009, 90: 465-473.
[19] Alshorbagy AE, Eltaher MA, Mahmoud FF. Free vibration characteristics of a functionally graded beam by finite element method. Applied Mathematical Modelling, 2011, 35: 412-425.
[20] Cook RD, Malkus DS, Plesha ME. Concepts and applications of finite element analysis (3^rd edn). John Wiley & Sons, Inc., Toronto, Canada, 1989.