Nonlinear vibration analysis of laminated plates restingon nonlinear two-parameters elastic foundations

Steel and Composite Structures

Volumn 11, Issue 5, 2011, Pages 403-421

  Akgöz, Bekir ^a   Civalek, Ömer ^a  

^a AKDENIZ UNIVERSITY   (Turkey)

Author keywords

Discrete singular convolution; Free vibration; Laminated plates; Nonlinear dynamics; Nonlinear foundation

Indexed keywords

CONVOLUTION; DYNAMICS; EQUATIONS OF MOTION; FOUNDATIONS; LAMINATING; NONLINEAR EQUATIONS; VIBRATIONS (MECHANICAL);

DISCRETE SINGULAR CONVOLUTION; FOUNDATION MODELING; FREE VIBRATION; GEOMETRICALLY NONLINEAR; GOVERNING EQUATIONS OF MOTION; LAMINATED PLATE; NON-LINEAR VIBRATIONS; NONLINEAR VIBRATION ANALYSIS;

VIBRATION ANALYSIS;

EID: 81455159262     PISSN: 12299367     EISSN: None     Source Type: Journal    
DOI: 10.12989/scs.2011.11.5.403     Document Type: Article

References (60)

1. Baltacolu, A.K. (2009), "Nonlinear static and dynamic analyses of laminated composite plates and shells restingon nonlinear elastic foundations", M.Sc. Seminar, Graduate school of natural and applied sciences, Akdeniz University, (in Turkish).
2. Bhaskar, A. and Dumir, P.C. (1988), "Nonlinear vibration of orthotropic thin rectangular plates on elastic foundations",J. Sound Vib., 125(1), 1-11.
3. Chen, C.S. and Fung, C.P. (2004), "Large-amplitude vibration of an initially stressed plate on elastic foundations",Comp. Struct., 82(9-10), 689-701.
4. Chien, R.D. and Chen, C.S. (2005), "Nonlinear vibration of laminated plates on a nonlinear elastic foundation", Compos. Struct., 70(1), 90-99.
5. Chien, R.D. and Chen, C.S. (2006), "Nonlinear vibration of laminated plates on an elastic foundation", Thin-WalledStruct., 44(8), 852-860.
6. Civalek, Ö. (2004), "Geometrically non-linear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ)", PhD. Thesis, Fýrat University, (in Turkish), Elaz.
7. Civalek, Ö. (2005), "Geometrically Nonlinear Dynamic Analysis of Doubly Curved Isotropic Shells Resting on Elastic Foundation by a Combination of HDQ-FD Methods", Int. J. Pressure Vessels and Piping, 82(6), 470-479. (Pubitemid 40451372)
8. Civalek, Ö. (2006), "Harmonic Differential Quadrature-Finite differences Coupled Approaches for Geometrically Nonlinear Static and Dynamic Analysis of Rectangular Plates on Elastic Foundation", J. Sound Vib., 294(4-5), 966-980.
9. Civalek, Ö. (2007a), "Nonlinear analysis of thin rectangular plates on Winkler-Pasternak elastic foundations by DSC-HDQ methods", Appl. Math. Model. 31(3), 606-624. (Pubitemid 44712654)
10. Civalek, Ö. (2007b), "Linear vibration analysis of isotropic conical shells by discrete singular convolution (DSC)", Struct. Eng. Mech., 25, 127-130. (Pubitemid 44920140)
11. Dai, K.Y., Liu, G.R., Lim, K.M. and Chen, X.L. (2004), "A mesh-free method for static and free vibration analysis of shear deformable laminated composite plates", J. Sound Vib., 269(3-5), 633-652.
12. Dumir, P.C. (1988), "Nonlinear dynamic response of isotropic thin rectangular plates on elastic foundations", Acta Mechanica, 71(1-4), 233-244. (Pubitemid 18607342)
13. Dumir, P.C. and Bhaskar, A. (1988), "Nonlinear static analysis of rectangular plates on elastic foundations by the orthogonal point collocation method", Comp. Meth. Appl. Mech. Eng., 67(1), 111-124. (Pubitemid 18574392)
14. Ganapathi, M., Varadan, T.K. and Sarma, B.S. (1991), "Nonlinear flexural vibrations of laminated orthotropic plates", Comp. Struct., 39(6), 685-688. (Pubitemid 21666158)
15. Kant, T., Arora, C.P. and Varaiya, J.H. (1992), "Finite element transient analysis of composite and sandwich plates based on a refined theory and mode superposition method", Compos. Struct., 22(2), 109-120. (Pubitemid 23560016)
16. Kant, T. and Kommineni, J.R. (1994), "Large amplitude free vibration analysis of cross-ply composite and sandwich laminates with a refined theory and C0 finite elements", Comp. Struct., 51(1), 123-134.
17. Kant, T. and Mallikarjuna, B.N. (1989), "Transient dynamic of composite sandwich plates using 4-, 8-, 9- noded isoparametric quadrilateral elements", Finite Elements in Anal. Design, 5(4), 307-318. (Pubitemid 20625123)
18. Kant, T., Ravichandran, R.V., Pandya, B.N. and Mallikarjuna, B.N. (1988), "Finite element transient dynamic analysis of isotropic and fibre reinforced composite plates using a higher-order theory", Compos. Struct., 9(4), 319-342. (Pubitemid 18623966)
19. Kant, T., Varaiya, J.H. and Arora, C.P. (1990), "Finite element transient analysis of composite and sandwich plates based on a refined theory and implicit time integration schemes", Comp. Struct., 36(3), 401-420. (Pubitemid 20736034)
20. Lai, S.K. and Xiang, Y. (2009), "DSC analysis for buckling and vibration of rectangular plates with elastically restrained edges and linearly varying in-plane loading", Int. J. Struct. Stab. Dynamics, 9(3), 511-531.
21. Liew, K.M., Han, J.-B. and Xiao, Z.M. (1996), "Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility", Int. J. Solids Struct., 33(18), 2647-2658. (Pubitemid 126382008)
22. Liew, K.M. and Huang, Y.Q. (2003), "Bending and buckling analysis of thick symmetric rectangular laminates using the moving least-squares differential quadrature method", Int. J. Mech. Sci., 45(1), 95-114.
23. Liew, K.M., Huang, Y.Q. and Reddy, J.N. (2003), "Vibration analysis of symmetrically laminated plates based FSDT using the moving least squares differential quadrature method", Comput. Meth. Appl. Mech. Eng., 192(19), 2203-2222. (Pubitemid 36669470)
24. Liew, K.M., Wang, J., Tan, M.J. and Rajendran, S. (2004), "Nonlinear analysis of laminated composite plates using the mesh-free kp-Ritz method based on FSDT", Comp. Meth. Appl. Mech. Eng., 193(45-47), 4763-4779. (Pubitemid 39408000)
25. Liew, K.M., Zhang, J.Z., Ng, T.Y. and Meguid, S.A. (2003), "Three-dimensional modeling of elastic bonding in composite laminates using layerwise differential quadrature", Int. J. Solids Struct., 40(7), 1745-1764. (Pubitemid 36352539)
26. Liu, G.R. and Achenbach, J.D. (1994), "A strip element method for stress analysis of anisotropic linearly elastic solid", ASME J. Appl. Mech., 61(2), 270-277.
27. Liu, G.R. and Chen, X.L. (2001), "A mesh free method for static and free vibration analysis of thin plates of arbitrary shape", J. Sound Vib., 241(5), 839-855. (Pubitemid 32370158)
28. Liu, G.R. and Chen, X.L. (2002), "Bucking of symmetrically laminated composite plates using the element-free Galerkin method", Int. J. Struct. Stab. Dynamics, 2(3), 281-294.
29. Manoj, T., Ayyappan, M., Krishnan, K.S. and Rao, B. N. (2000), "Nonlinear vibration analysis of thin laminated rectangular plates on elastic foundations", ZAMM, 80(3), 183-192.
30. Nath, Y., Kumar, S. (1995a), "Chebyshev series solution to nonlinear boundary value problems in rectangular domain", Comp. Meth. Appl. Mech. Eng., 125(1-4), 41-52.
31. Nath, Y., Prithviraju, M. and Mufti, A.A. (2006), "Nonlinear static and dynamics of antisymmetric composite laminated square plates supported on nonlinear elastic subgrade", Commun. Nonlinear Sci. Numer. Simulat., 11(3),340-354. (Pubitemid 41448052)
32. Nath, Y. and Shukla, K.K. (2001), "Non-linear transient analysis of moderately thick laminated composite plates", J. Sound. Vib., 273(3), 509-526. (Pubitemid 33018045)
33. Nath, Y., Varma, K.K. and Mahrenholtz, D. (1986), "Nonlinear Dynamic response of rectangular plates on linear elastic foundation", Comp. Struct., 24(3), 391-399. (Pubitemid 17492105)
34. Seçkin, A. and Sarýgül, A.S. (2009a), "Free vibration analysis of symmetrically laminated thin composite plates by using discrete singular convolution (DSC) approach: Algorithm and verification", J. Sound Vib. 315(1-2), 197-211.
35. Seçkin, A. and Sarýgül, A.S. (2009b), "A novel scheme for the discrete prediction of high-frequency vibration response: Discrete singular convolution-mode superposition approach", J. Sound Vib., 320(4-5), 1004-1022.
36. Shen, H.-S. (1999), "Large deflection of composite laminated plates under transverse and in-plane loads resting on elastic foundation", Compos. Struct., 45(2), 115-123.
37. Shen, H.-S. (2000a), "Nonlinear analysis of composite laminated thin plates subjected to lateral pressure and thermal loading and resting on elastic foundations", Compos. Struct., 49(2), 115-128. (Pubitemid 30585390)
38. Shen, H.-S. (2000b), "Nonlinear bending of shear deformable laminated plates under transverse and in-plane loads resting on elastic foundation", Compos. Struct., 50(2), 131-142.
39. Shen, H.-S. (2000c), "Nonlinear bending of shear deformable laminated plates under lateral pressure and thermal loading and resting on elastic foundations", J. Strain Analy., 35(2), 93-108. (Pubitemid 30590653)
40. Shih, Y.-S. and Blotter, P.T. (1993), "Non-linear vibration analysis of arbitrarily laminated thin rectangular plates on elastic foundations", J. Sound Vib., 167(3), 433-459.
41. Shukla, K.K. and Nath, Y. (2000), "Non-linear analysis of moderately thick laminated rectangular plates", J. Eng. Mech. ASCE, 26, 831-838.
42. Shukla, K.K., Nath, Y. and Kreuzer, E. (2005), "Buckling and transient behaviour of layered composite plates under thermomechanical loading", ZAMM Journal, 85(3), 163-175. (Pubitemid 40419323)
43. Sofiyev, A.H. (2010), "Buckling analysis of FGM circular shells under combined loads and resting on the Pasternak type elastic foundation", Mech. Research Commun, 37(6), 539-544.
44. Teo, T.M. and Liew, K.M. (2002), "Differential cubature method for analysis of shear deformable rectangular plates on Pasternak foundations", Int. J. Mech. Sci., 44(6), 1179-1194. (Pubitemid 34715776)
45. Wang, Y.Y., Lam, K.Y. and Liu, G.R. (2000), "Bending Analysis of Classical Symmetric Laminated Plates by the Strip Element Method", Mech. Compos. Mater. Struct. 7(3), 225-247.
46. Wang, Y.Y., Lam, K.Y, and Liu, G. R. (2001), "A Strip Element Method for the Transient Analysis of Symmetric Laminated Plates", Int. J. Solids Struct., 38(2), 241-259. (Pubitemid 32035081)
47. Wei, G.W. (1999), "Discrete singular convolution for the solution of the Fokker-Planck equations", J. Chem. Phys., 110, 8930-8942.
48. Wei, G.W. (2001a), "A new algorithm for solving some mechanical problems", Comp. Meth. Appl. Mech. Eng., 190(15-17), 2017-2030. (Pubitemid 32337550)
49. Wei, G.W. (2001b), "Discrete singular convolution for beam analysis", Eng. Struct., 23(9), 1045-1053. (Pubitemid 32719260)
50. Wei, G.W., Kouri, D.J. and Hoffman, D.K. (1998), "Wavelets and distributed approximating functionals", Comp. Phys. Commun., 112(1), 1-6.
51. Wei, G.W., 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(8), 1731-1746. (Pubitemid 32544281)
52. Wei, G.W., 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(8), 913-946. (Pubitemid 35206179)
53. Wei, G.W., Zhao, Y.B. and Xiang, Y. (2002b), "A novel approach for the analysis of high-frequency vibrations", J. Sound Vib., 257(2), 207-246. (Pubitemid 35433966)
54. Xiang, Y., Lai, S.K. and Zhou, L. (2010), "DSC-element method for free vibration analysis of rectangular Mindlin plates", Int. J. Mech. Sci., 52(4), 548-560.
55. Xiang, Y., Lai, S.K., Zhou, L. and Lim, C.W. (2010), "DSC-Ritz element method for vibration analysis of rectangular Mindlin plates with mixed edge supports", Eur. J. Mech. A/Solids, 29(4), 619-628.
56. Xiang, Y., Zhao, Y.B. and Wei, G.W. (2002), "Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications", Int. J. Numer. Meth. Eng., 55(8), 947-971. (Pubitemid 35206180)
57. Zhao, S. and Wei, G.W. (2003), "Comparison of the discrete singular convolution and three other numerical schemes for solving Fisher's equation", SIAM J. Sci. Comput., 25(1), 127-147.
58. Zhao, S., Wei, G.W. and Xiang, Y. (2005), "DSC analysis of free-edged beams by an iteratively matched boundarymethod", J. Sound Vib., 284(1-2), 487-493. (Pubitemid 40539066)
59. Zhao, Y.B. and Wei, G.W. (2002), "DSC analysis of rectangular plates with non-uniform boundary conditions", J. Sound Vib., 255(2), 203-228.
60. Zhao, Y.B., Wei, G.W. and Xiang, Y. (2002a), "Discrete singular convolution for the prediction of high frequency vibration of plates", Int. J. Solids Struct., 39(1), 65-88. (Pubitemid 34021246)