The determination of frequencies of laminated conical shells via the discrete singular convolution method

Journal of Mechanics of Materials and Structures

Volumn 1, Issue 1, 2006, Pages 163-182

  Civalek, Ömer ^a  

^a AKDENIZ UNIVERSITY   (Turkey)

Author keywords

Conical shells; Discrete singular convolution; Frequencies; Laminated composite

Indexed keywords

ALGEBRA; APPROXIMATION ALGORITHMS; EQUATIONS OF MOTION; LAMINATED COMPOSITES; LAMINATING; SHELLS (STRUCTURES); VIBRATION ANALYSIS;

ALGEBRAIC EQUATIONS; COMPARISON STUDY; DISCRETE SINGULAR CONVOLUTION; FREE VIBRATION; GOVERNING DIFFERENTIAL EQUATIONS; LAMINATED CONICAL SHELLS; NUMERICAL SOLUTION; THIN SHELL THEORY;

CONVOLUTION;

EID: 33847688895     PISSN: 15593959     EISSN: None     Source Type: Journal    
DOI: 10.2140/jomms.2006.1.163     Document Type: Article

References (45)

1. M. Bacon and C. W. Bert, "Unsymmetric free vibrations of orthotopic sandwich shells of revolution", AIAA J. 5:3 (1967), 413-417.
2. C. H. Chang, "Vibration of conical shells", Shock Vib. Dig. 13:1 (1981), 9-17.
3. Ö. Civalek, "Finite-element analyses of plates and shells", Firat University, Elazig, 1998. In Turkish.
4. Ö. Civalek, Geometrically non-linear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ), Ph.D. thesis, Firat University, Elazig, 2004. In Turkish.
5. Ö. Civalek, "Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of HDQ-FD methods", Int. J. Pressure Vessels Piping 82:6 (2005), 470-179.
6. Ö. Civalek and M. Ülker, "HDQ-FD integrated methodology for nonlinear static and dynamic response of doubly curved shallow shells", Int. J. Struct. Engin. Mech. 19:5 (2005), 535-550.
7. L. Hua, "Frequency characteristics of a rotating truncated circular layered conical shell", Compos. Struct. 50:1 (2000), 59-68.
8. L. Hua and K. Y. Lam, "The generalized differential quadrature method for frequency analysis of a rotating conical shell with initial pressure", Int. J. Numer. Meth. Eng. 48:12 (2000), 1703-1722.
9. T. Irie, G. Yamada, and Y. Kaneko, "Free vibration of a conical shell with variable thickness", J. Sound Vib. 82:1 (1982), 83-94.
10. T. Irie, G. Yamada, and K. Tanaka, "Natural frequencies of truncated conical shells", J. Sound Vib. 92:3 (1984), 447-453.
11. R. K. Kapania, "A review on the analysis of laminated shells", J. Pressure Vessel Technol. (ASME) 111 (1989), 88-96.
12. K. Y. Lam and L. Hua, "Vibration analysis of a rotating truncated circular conical shell", Int. J. Solids Struct. 34:17 (1997), 2183-2197.
13. A. W. Leissa, "Vibration of shells", NASA, 1973.
14. K. M. Liew and C. W. Lim, "Vibratory characteristics of cantilevered rectangular shallow shells of variable thickness", A1AA J. 32:2 (1994), 387-396.
15. K. M. Liew, M. K. Lim, C. W. Lim, D. B. Li, and Y. R. Zhang, "Effects of initial twist and thickness variation on the vibration behaviour of shallow conical shells", J. Sound Vib. 180:2 (1995), 271-296.
16. K. M. Liew, T. Y. Ng, and X. Zhao, "Free vibration analysis of conical shells via the element-free kp-Ritz method", J. Sound Vib. 281:3-5 (2005), 627-645.
17. C. W. Lim and S. Kitipornchai, "Effects of subtended and vertex angles on the free vibration of open conical shell panels: a conical co-ordinate approach", J. Sound Vib. 219:5 (1999), 813-835.
18. C. W. Lim and K. M. Liew, "Vibratory behaviour of shallow conical shells by a global Ritz formulation", Eng. Struct. 17:1 (1995), 63-70.
19. C. W. Lim, K. M. Liew, and S. Kitipornchai, "Free vibration of pretwisted, cantilevered composite shallow conical shells", AIAA J. 35:2 (1997), 327-333.
20. C. W. Lim, K. M. Liew, and S. Kitipornchai, "Vibration of cantilevered laminated composite shallow conical shells", Int. J. Solids Struct. 35:15 (1998), 1695-1707.
21. C. W. Lim, Z. R. Li, and G. W. Wei, "DSC-Ritz method for high-mode frequency analysis of thick shallow shells", Int. J. Numer. Meth. Eng. 62:2 (2005), 205-232.
22. C. W. Lim, Z. R. Li, Y. Xiang, G. W. Wei, and C. Wang, "On the missing modes when using the exact frequency relationship between Kirchhoff and Mindlin plates", Adv. Vib. Eng. 4 (2005), 221-248.
23. A. E. H. Love, "On the small free vibrations and deformations of thin elastic shells", Philos. T. Roy. Soc. A 179A (1888), 491-546.
24. C. Shu, "An efficient approach for free vibration analysis of conical shells", Int. J. Mech. Sci. 38:8-9 (1996), 935-949.
25. C. Shu, "Free vibration analysis of composite laminated conical shells by generalized differential quadrature", J. Sound Vib. 194:4 (1996), 587-604.
26. C. Shu and H. Du, "Free vibration analysis of laminated composite cylindrical shells by DQM", Compos. B: Eng. 28:3 (1997), 267-274.
27. C. C. Siu and C. W. Bert, "Free vibrational analysis of sandwich conical shells with free edges", J. Acoust. Soc. Am. 47:3B (1970), 943-945.
28. K. R. Sivadas and N. Ganesan, "Vibration analysis of thick composite clamped conical shells of varying thickness", J. Sound Vib. 152:1 (1992), 27-37.
29. W. Soedel, Vibrations of shells and plates, 2nd ed., Marcel Dekker, New York, 1996.
30. L. Tong, "Free vibration of composite laminated conical shells", Int. J. Mech. Sci. 35:1 (1993), 47-61.
31. L. Tong, "Free vibration of orthotropic conical shells", Int. J. Eng. Sci. 31:5 (1993)
32. L. Tong and T. K. Wang, "Simple solutions for buckling of laminated conical shells", Int. J. Mech. Sci. 34:2 (1992), 93-111.
33. D. C. Wan, Y. C. Zhou, and G. W. Wei, "Numerical solution of incompressible flows by discrete singular convolution", Int. J. Numer. Meth. Fl. 38:8 (2002), 789-810.
34. G. W. Wei, "Discrete singular convolution for the solution of the Fokker-Planck equation", J. Chem. Phys. 110:18 (1999), 8930-8942.
35. G. W. Wei, "A new algorithm for solving some mechanical problems", Comput. Methods Appl. Mech. Eng. 190:15-17 (2001), 2017-2030.
36. G. W. Wei, "Vibration analysis by discrete singular convolution", J. Sound Vib. 244:3 (2001), 535-553.
37. G. W. Wei, Y. B. Zhao, and Y. Xiang, "Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm", Int. J. Numer. Meth Eng. 55:8 (2002), 913-946.
38. G. W. Wei, Y. B. Zhao, and Y. Xiang, "A novel approach for the analysis of high-frequency vibrations", J. Sound Vib. 257:2 (2002), 207-246.
39. C. P. Wu and C. Y. Lee, "Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness", Int. J. Mech. Sci. 43:8 (2001), 1853-1869.
40. C. P. Wu and C. H. Wu, "Asymptotic differential quadrature solutions for the free vibration of laminated conical shells", Comput. Mech. 25:4 (2000), 346-357.
41. C. C. Yang, "On vibrations of orthotropic conical shells", J. Sound Vib. 34 (1974), 552-555.
42. Y. B. Zhao and G. W. Wei, "DSC analysis of rectangular plates with nonuniform boundary conditions", J. Sound Vib. 255:2 (2002), 203-228.
43. Y. B. Zhao, G. W. Wei, and Y. Xiang, "Discrete singular convolution for the prediction of high frequency vibration of plates", Int. J. Solids Struct. 39:1 (2002), 65-88.
44. S. Zhao, G. W. Wei, and Y. Xiang, "DSC analysis of free-edged beams by an iteratively matched boundary method", J. Sound Vib. 284:1-2 (2005), 487-493.
45. Y. C. Zhou, S. Zhao, M. Feig, and G. W. Wei, "High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources", J. Comput. Phys. 213:1 (2006), 1-30.