Free vibration and buckling analyses of functionally graded beams with edge cracks

Composite Structures

Volumn 83, Issue 1, 2008, Pages 48-60

  Yang, J ^a   Chen, Y ^a,b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b BEIJING JIAOTONG UNIVERSITY   (China)

Author keywords

Beam; Buckling; Functionally graded materials; Open edge crack; Vibration

Indexed keywords

BUCKLING; CRACKS; FUNCTIONALLY GRADED MATERIALS; NATURAL FREQUENCIES; SUPPORTS; VIBRATIONS (MECHANICAL);

BERNOULLI-EULER BEAM THEORY; FREE VIBRATION; OPEN EDGE CRACK; SLENDERNESS RATIO;

BEAMS AND GIRDERS;

BEAM; BUCKLING; CRACKING; LOADING (TESTING); VIBRATION;

EID: 36749048659     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2007.03.006     Document Type: Article

References (37)

1. Dimarogonas A.D. Vibration of cracked structures: a state of the art review. Eng Fract Mech 55 5 (1996) 831-857
2. Gounaris G.D., Papadopoulos C.A., and Dimarogonas A.D. Crack identification in beams by coupled response measurement. Comput Struct 58 2 (1996) 299-305
3. Chondros T.G., Dimarogonas A.D., and Yao J. A continuous cracked beam vibration theory. J Sound Vib 215 1 (1998) 17-34
4. Shifrin E.I., and Ruotolo R. Natural frequencies of a beam with an arbitrary number of cracks. J Sound Vib 222 3 (1999) 409-423
5. Binici B. Vibration of beams with multiple open cracks subjected to axial force. J Sound Vib 287 1-2 (2005) 277-295
6. Yokoyama T., and Chen M.C. Vibration analysis of edge-cracked beams using a line-spring model. Eng Fract Mech 59 3 (1998) 403-409
7. Zheng D.Y., and Fan S.C. Natural frequency changes of a cracked timoshenko beam by modified Fourier series. J Sound Vib 246 2 (2001) 297-317
8. Hsu M.H. Vibration analysis of edge-cracked beam on elastic foundation with axial loading using the differential quadrature method. Comput Methods Appl Mech Eng 194 1 (2005) 1-17
9. El Bikri K., Benamar R., and Bennouna M.M. Geometrically non-linear free vibrations of clamped-clamped beams with an edge crack. Comput Struct 84 7 (2006) 485-502
10. Wang Q. A comprehensive stability analysis of a cracked beam subjected to follower compression. Int J Solids Struct 41 18-19 (2004) 4875-4888
11. Zhou L., and Huang Y. Crack effect on the elastic buckling behavior of axially and eccentrically loaded columns. Struct Eng Mech 22 2 (2006) 169-184
12. Wang Q., and Quek S.T. Repair of cracked column under axially compressive load via piezoelectric patch. Comput Struct 83 15-16 (2005) 1355-1363
13. Noda N. Thermal stresses in functionally graded materials. J Thermal Stresses 22 4-5 (1999) 477-512
14. Liew K.M., Kitipornchai S., Zhang X.Z., and Lim C.W. Analysis of the thermal stress behavior of functionally graded hollow circular cylinders. Int J Solids Struct 40 10 (2003) 2355-2380
15. Qian L.F., and Batra R.C. Transient thermoelastic deformations of a thick functionally graded plate. J Thermal Stresses 27 8 (2004) 705-740
16. Ootao Y., and Tanigawa Y. Transient thermoelastic problem of functionally graded thick strip due to nonuniform heat supply. Compos Struct 63 2 (2004) 139-146
17. Jin Z.H., and Batra R.C. Some basic fracture mechanics concepts in functionally graded materials. J Mech Phy Solids 44 8 (1996) 1221-1235
18. Erdogan F., and Wu B.H. The surface crack problem for a plate with functionally graded properties. J Appl Mech ASME 64 3 (1997) 448-456
19. Wang B.L., and Noda N. Thermally induced fracture of a smart functionally graded composite structure. Theor Appl Fract Mech 35 2 (2001) 93-109
20. Guo L.C., Wu L.Z., Zeng T., and Ma L. The dynamic fracture behavior of a functionally graded coating-substrate system. Compos Struct 64 3-4 (2004) 433-441
21. Yang J., and Shen H.S. Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions. Compos Part B 34 2 (2003) 103-115
22. Ma L.S., and Wang T.J. Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings. Int J Solids Struct 40 13-14 (2003) 3311-3330
23. Yang J., Kitipornchai S., and Liew K.M. Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators. Int J Numer Methods Eng 59 12 (2004) 1605-1632
24. Ferreira A.J.M., Batra R.C., Roque C.M.C., Qian L.F., and Martins P.A.L.S. Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method. Compos Struct 69 4 (2005) 449-457
25. Praveen G.N., and Reddy J.N. Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. Int J Solids Struct 35 33 (1998) 4457-4476
26. Reddy J.N. Analysis of functionally graded plates. Int J Numer Methods Eng 47 1-3 (2000) 663-684
27. Vel S.S., and Batra R.C. Three-dimensional exact solution for the vibration of functionally graded rectangular plates. J Sound Vib 272 3-5 (2004) 703-730
28. Kitipornchai S., Yang J., and Liew K.M. Random vibration of functionally graded laminates in thermal environments. Comput Methods Appl Mech Eng 195 9-12 (2005) 1075-1095
29. Yang J., and Shen H.S. Dynamic response of initially stressed functionally graded rectangular thin plates. Compos Struct 54 4 (2001) 497-508
30. Liew K.M., Yang J., and Kitipornchai S. Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading. Int J Solids Struct 40 (2003) 3869-3892
31. Yang J., Liew K.M., and Kitipornchai S. Second-order statistics of the elastic buckling of functionally graded rectangular plates. Compos Sci Technol 65 7-8 (2005) 1165-1175
32. Shen H.S. Postbuckling of axially loaded FGM hybrid cylindrical shells in thermal environments. Compos Sci Technol 65 11-12 (2005) 1675-1690
33. Na K.S., and Kim J.H. Three-dimensional thermomechanical buckling analysis for functionally graded composite plates. Compos Struct 73 4 (2006) 413-422
34. Ootao Y., and Tanigawa Y. Three-dimensional transient piezothermoelasticity in functionally graded rectangular plate bonded to a piezoelectric plate. Int J Solids Struct 37 32 (2000) 4377-4401
35. Reddy J.N., and Chen Z.Q. Three-dimensional solutions of smart functionally graded plates. J Appl Mech ASME 68 2 (2000) 234-241
36. Kapuria S., Bhattacharyya M., and Kumar A.N. Assessment of coupled ID models for hybrid piezoelectric layered functionally graded beams. Compos Struct 72 4 (2006) 455-468
37. Broek D. Elementary Engineering Fracture Mechanics (1986), Martinus Nijhoff