Vibration analysis of plates with curvilinear quadrilateral domains by discrete singular convolution method

Structural Engineering and Mechanics

Volumn 36, Issue 3, 2010, Pages 279-299

  Civalek, Ömer ^a   Ozturk, Baki ^b  

^a AKDENIZ UNIVERSITY   (Turkey)

^b NIGDE UNIVERSITY   (Turkey)

Author keywords

Curvilinear domain; Discrete singular convolution; Natural frequency; Numerical models; Plates

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; CONVOLUTION; MATHEMATICAL TRANSFORMATIONS; NATURAL FREQUENCIES; NUMERICAL MODELS; PLATING;

ANALYTICAL METHOD; CO-ORDINATE TRANSFORMATION; CURVILINEAR DOMAINS; DIFFERENT GEOMETRY; DISCRETE SINGULAR CONVOLUTION; FREE-VIBRATION ANALYSIS; GOVERNING EQUATIONS; RECTANGULAR DOMAIN;

VIBRATION ANALYSIS;

EID: 77957305383     PISSN: 12254568     EISSN: None     Source Type: Journal    
DOI: 10.12989/sem.2010.36.3.279     Document Type: Article

References (63)

1. Bert, C.W. and Malik, M. (1996), "The differential quadrature method for irregular domains and application to plate vibration", Int. J. Mech. Sci., 38(6), 589-606. (Pubitemid 126652141)
2. Cheung, Y.K., Tham, L.G and Li, W.Y. (1988), "Free vibration and static analysis of general plates by spline finite strip method", Comput. Mech., 3, 187-197.
3. Cheung, Y.K. and Cheung, M.S. (1971), "Flexural vibrations of rectangular and other polygonal plates", J. Eng. Mech., 97, 3911-411.
4. Civalek, Ö. (2004), "Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns", Eng. Struct., 26(2), 171-186.
5. Civalek, Ö. (2005), "Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of harmonic differential quadrature-finite difference methods", Int. J. Pres. Ves. Pip., 82(6), 470-479.
6. Civalek, Ö. (2006), "An efficient method for free vibration analysis of rotating truncated conical shells", Int. J. Pres. Ves. Pip., 83, 1-12. (Pubitemid 43168973)
7. Civalek, Ö. (2007a), "Nonlinear analysis of thin rectangular plates on Winkler-Pasternak elastic foundations by DSC-HDQ methods", Appl. Math. Model., 31, 606-624.
8. Civalek, Ö. (2007b), "Frequency analysis of isotropic conical shells by discrete singular convolution (DSC)", Struct. Eng. Mech., 25( 1 ), 127-130.
9. Civalek, Ö. (2007c), "Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: discrete singular convolution (DSC) approach", J. Comput. Appl. Math., 205, 251-271. (Pubitemid 46656438)
10. Civalek, Ö. (2007d), "A parametric study of the free vibration analysis of rotating laminated cylindrical shells using the method of discrete singular convolution", Thin Wall. Struct., 45, 692-698.
11. Geannakakes, GN. (1990), "Vibration analysis of arbitrarily shaped plates using beam characteristics orthogonal polynomials in semi-analytical finite strip method", J. Sound Vib., 137, 283-303.
12. Gordon, W.J. and Hall, C.A. (1973), "Construction of curvilinear co-ordinate systems and application to mesh generation", Int. J. Numer. Meth. Eng., 7, 461-477.
13. Gorman, D.J. (1988), "Accurate free vibration analysis of rhombic plates with simply-supported and fully- clamped edge conditions", J. Sound Vib., 125, 281-290.
14. Han, J.B. and Liew, K.M. (1997), "An eight-node curvilinear differential quadrature formulation for Reissner/Mindlin plates", Comput. Meth. Appl. Mech. Eng., 141, 265-280.
15. Huang, C.S., Leissa, A.W. and McGee, O.G (1993), "Exact analytical solutions for free vibrations of sectorial plates with simply supported radial edges", J. Appl. Mech., 60, 478-483.
16. Karami, G and Malekzadeh, P. (2003), "An efficient differential quadrature methodology for free vibration analysis of arbitrary straight-sided quadrilateral thin plates", J. Sound Vib., 263, 415-442.
17. Lam, K.Y., Liew, K.M. and Chow, S.T. (1992), "Use of two-dimensional orthogonal polynomials for vibration analysis of circular and elliptical plates", J. Sound Vib., 154, 261-269.
18. Lam, K.Y., Liew, K.M. and Chow, S.T. (1990), "Free vibration analysis of isotropic and orthotopic triangular plates", Int. J. Mech. Sci., 32(5), 455-464.
19. Leissa, A.W. (1969), Vibration of Plates, NASA, SP-160.
20. Leissa, A.W. (1977), "Recent research in plate vibrations: complicating effects", Shock Vib., 9(11), 21-35.
21. Leissa, A.W. (1981), "Plate vibration research, 1976-1980: classical theory", Shock Vib., 13(9), 11-12.
22. Leissa, A.W. (1987), "Recent research in plate vibrations: 1981-1985: Part I. classical theory", Shock Vib., 19(2), 11-18.
23. Leissa, A.W., McGee, O.G and Huang, C.S. (1993), "Vibrations of sectorial plates having corner stress singularities", J. Appl. Mech., 60, 131-140.
24. Li, W.Y., Cheung, Y.K. and Tham, L.G (1986), "Spline finite strip analysis of general plates", J. Eng. Mech., 112(1), 43-54.
25. Liew, K.M. and Han, J.B. (1997), "A four-note differential quadrature method for straight-sided quadrilateral Reissner/Mindlin plates", Commun. Numer. Meth. Eng., 13, 73-81.
26. Liew, K.M. (1992), "Frequency solutions for circular plates with internal supports and discontinuous boundaries", Int. J. Mech. Sci., 34(7), 511-520.
27. Liew, K.M., Xiang, Y. and Kitipornchai, S. (1995), "Benchmark vibration solutions for regular polygonal Mindlin plates", J. Acoust. Soc. Am., 97(5), 2866-2871.
28. Liew, K.M. and Lam, K.Y. (1993a), "On the use of 2-D orthogonal polynomials in the Rayleigh-Ritz method for flexural vibration of annular sector plates of arbitrary shape", Int. J. Mech. Sci., 35, 129-139.
29. Liew, K.M. and Lam, K.Y. (1993b), "Transverse vibration of solid circular plates continuous over multiple concentric annular supports", J. Appl. Mech., 60, 208-210.
30. Liew, K.M., Lim, C.W. and Lim, M.K. (1994), "Transverse vibration of trapezoidal plates of variable thickness: unsymmetric trapezoids", J. Sound Vib., 177(4), 479-501.
31. Liew, K.M. and Sumi, Y.K. (1998), "Vibration of plates having orthogonal straight edges with clamped boundaries", J. Eng. Mech., 124, 184-192.
32. Liew, K.M., Lam, K.Y. and Chow, S.T. (1990), "Free vibration analysis of rectangular plates using orthogonal plate function", Comp. Struct., 34(1), 79-85.
33. Liew, K.M. and Lam, K.Y. (1990), "Application of two-dimensional orthogonal plate function to flexural vibration of skew plates", J. Sound Vib., 139(2), 241-252.
34. Liew, K.M. and Lam, K.Y. (1991), "A Rayleigh-Ritz approach to transverse vibration of isotropic and anisotropic trapezoidal plates using orthogonal plate functions", Int. J. Solids Struct., 27(2), 189-203.
35. Liew, K.M. (1993a), "On the use of pb-2 Rayleigh-Ritz method for free flexural vibration of triangular plates with curved internal supports", J. Sound Vib., 165(2), 329-340.
36. Liew, K.M. (1993b), "Treatments of over-restrained boundaries for doubly connected plates of arbitrary shape in vibration analysis", Int. J. Solids Struct., 30(3), 337-347.
37. Liew, K.M. and Lim, M.K. (1993), "Transverse vibration of trapezoidal plates of variable thickness: symmetric trapezoids", J. Sound Vib., 165(1), 45-67.
38. Lim, C.W., Li, Z.R., Xiang, Y., Wei, GW. and Wang, C.M. (2005a), "On the missing modes when using the exact frequency relationship between Kirchhoff and Mindlin plates", Adv. Vib. Eng., 4, 221-248.
39. Lim, C.W., Li, Z.R. and Wei, GW. (2005b), "DSC-Ritz method for high-mode frequency analysis of thick shallow shells", Int. J. Numer. Meth. Eng., 62, 205-232.
40. Liu, F.L. and Liew, K.M. (1999), "Free vibration analysis of Mindlin sector plates: numerical solutions by differential quadrature method", Comput. Meth. Appl. Mech. Eng., 177, 77-92.
41. Malik, M. and Bert, C.W. (2000), "Vibration analysis of plates with curvilinear quadrilateral planforms by DQM using blending functions", J. Sound Vib., 230(4), 949-954.
42. Ng, C.H.W., Zhao, Y.B. and Wei, GW. (2004), "Comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates", Comput. Meth. Appl. Mech. Eng., 193, 2483-2506.
43. Shu, C., Chen, W. and Du, H. (2000), "Free vibration analysis of curvilinear quadrilateral plates by the differential quadrature method", J. Comput. Phys., 163, 452-466.
44. Singh, B. and Chakraverty, S. (1992), "On the use of orthogonal polynomials in the Rayleigh-Ritz method for study of transverse vibration of elliptic plates", Comp. Struct., 43, 439-443.
45. Wang, C.M., Xiang, Y., Watanabe, E. and Utsunomiya, T. (2004), "Mode shapes and stress-resultants of circular Mindlin plates with free edges", J. Sound Vib., 276(3-5), 511-525.
46. Wang, C.M. (1994), "Natural frequencies formula for simply supported Mindlin plates", J. Vib. Acoust., 116(4), 536-540.
47. Wang, C.M., Xiang, Y., Utsunomiya, T. and Watanabe, E. (2001), "Evaluation of modal stress resultants in freely vibrating plates", Int. J. Solids Struct., 38(36-37), 6525-6558.
48. Wang, G and Cheng-Tzu, T.H. (1994), "Static and dynamic analysis of arbitrary quadrilateral flexural plates by B3-spline functions", Int. J. Solids Struct., 31, 657-667.
49. Wang, X., Striz, A.G and Bert, C.W. (1994), "Buckling and vibration analysis of skew plates by the differential quadrature method", AIAA J., 32(4), 886-889.
50. Wei, GW., Kouri, D.J. and Hoffman, D.K. (1998), "Wavelets and distributed approximating functional", Comput. phys. Commun., 112, 1-6.
51. Wei, GW. (1999), "Discrete singular convolution for the solution of the Fokker-Planck equations", J. Chem. Phys., 110, 8930-8942.
52. Wei, GW. (2001a), "A new algorithm for solving some mechanical problems", Comput. Meth. Appl. Mech. Eng., 190, 2017-2030.
53. Wei, GW. (2001b), "Vibration analysis by discrete singular convolution", J. Sound Vib., 244, 535-553.
54. Wei, GW. (2001c), "Discrete singular convolution for beam analysis", Eng. Struct., 23, 1045-1053.
55. Wei, GW., Zhao, Y.B. and Xiang, Y. (2001), "The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution", Int. J. Mech. Sci., 43, 1731-1746.
56. Wei, GW. and Gu, Y. (2002), "Conjugate filter approach for solving Burgers' equation", J. Comput. Appl. Math., 149, 439-456.
57. Wei, GW., Zhao, Y.B. and Xiang, Y. (2002a), "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, 913-946. (Pubitemid 35206179)
58. Wei, GW., Zhao, Y.B. and Xiang, Y. (2002b), "A novel approach for the analysis of high-frequency vibrations", J. Sound Vib., 257(2), 207-246.
59. Wu, W.X., Shu, C. and Wang, C.M. (2006), "Computation of modal stress resultants for completely free vibrating plates by LSFD method", J. Sound Vib., 297, 704-726.
60. Xiang, Y., Liew, K.M. and Kitipornchai, S. (1993), "Transverse vibration of thick annular sector plates", J. Eng. Mech., 119, 1579-1599.
61. Zhao, Y.B., Wei, GW. and Xiang, Y. (2002), "Discrete singular convolution for the prediction of high frequency vibration of plates", Int. J. Solids Struct., 39, 65-88.
62. Zhao, Y.B. and Wei, GW. (2002), "DSC analysis of rectangular plates with non-uniform boundary conditions", J.Sound Vib., 255(2), 203-228.
63. Zhao, S., Wei, GW. and Xiang, Y. (2005), "DSC analysis of free-edged beams by an iteratively matched boundary method", J. Sound Vib., 284, 487-493.