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Advances in Vibration, Buckling and Postbuckling Studies on Composite Plates

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Composite Structures

Abstract

Advances in the understanding of vibration and buckling behavior of laminated plates made of filamentary composite material are summarized in this survey paper. Depending upon the number of laminae and their orientation, vibration and buckling analyses of composite plates may be treated with: (7) orthotropic theory, (2) anisotropic theory, or (3) more complicated, general theory involving coupling between bending and stretching of the plate. The emphasis of the present overview is upon the last. Special consideration is given to the complicating effects of: inplane initial stresses, large amplitude (nonlinear) transverse displacements, shear deformation, rotary inertia, effects of surrounding media, inplane nonhomogeneity and variable thickness. Nonclassical buckling considerations such as initial imperfections are included, as well as postbuckling behavior.

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References

  1. Leissa, A. W., Vibration of plates, NASA SP-160, Washington, DC, US Govt. Printing Off., 1969.

    Google Scholar 

  2. Reissner, E. and Stavsky, Y., Bending and stretching of certain types of heterogeneous aeolotropic elastic plates, Trans. ASME, J. Appl. Mech., 28 (1961) 402–8.

    Article  Google Scholar 

  3. Stavsky, Y., On the theory of heterogeneous anisotropic plates, D.Sc. Thesis, Mass. Inst. of Tech., 1959.

    Google Scholar 

  4. Ashton, J. E. and Whitney, J. M., Theory of laminated plates, Stamford, Conn., Technomic Publishing, 1970.

    Google Scholar 

  5. Jones, R. M., Mechanics of composite materials, New York, McGraw-Hill, 1975.

    Google Scholar 

  6. Bert, C. W., Dynamics of composite and sandwich panels. Part I, Shock Vib. Dig., 8 (1976)37–48.

    Article  Google Scholar 

  7. Bert, C. W., Dynamics of composite and sandwich panels. Part II, Shock Vib. Dig., 8 (1976) 15–24.

    Article  Google Scholar 

  8. Bert, C. W., Recent research in composite and sandwich plate dynamics, Shock Vib. Dig., 11 (1979) 13–23.

    Article  Google Scholar 

  9. Bert, C. W., Vibration of composite structures, Proc. of the Inter. Conf. on Recent Advances in Structural Dynamics, University of Southampton, Southampton, England, July 7-11, 1980.

    Google Scholar 

  10. Bert, C. W. and Francis, P. H., Composite material mechanics: structural mechanics, AIAA 7., 12 (1974) 1173–86.

    Article  Google Scholar 

  11. Leissa, A. W., Recent research in plate vibrations. 1973-1976: complicating effects, Shock Vib. Dig., 10 (1978) 21–35.

    Article  Google Scholar 

  12. Bert, C. W., Fundamental frequencies of orthotropic plates with various planforms and edge conditions, Shock Vib. Bull., 47 (1977) 89–94.

    Google Scholar 

  13. Ashton, J. E. and Waddoups, M. E., Analysis of anisotropic plates, J. Composite Mat., 3 (1969) 148–65.

    Article  Google Scholar 

  14. Whitney, J. M., Fourier analysis of clamped anisotropic plates, Trans. ASME, J. Appl. Mech., 38 (1971) 530–2.

    Article  Google Scholar 

  15. Whitney, J. M., On the analysis of anisotropic rectangular plates, Air Force Materials Lab. Report TR-72-76, 1972, 24 pp.

    Google Scholar 

  16. Bert, C. W., Optimal design of a composite-material plate to maximize its fundamental frequency, J. Sound Vib., 50 (1977) 229–37.

    Article  Google Scholar 

  17. Bert, C. W., Optimal design of composite-material panels for business aircraft, Presented at Society of Automotive Engineers Business Aircraft Meeting, Wichita, Kansas, Mar. 29-Apr. 1, 1977.

    Google Scholar 

  18. Rajamani, A. and Prabhakaran, R., Dynamic response of composite plates with cut-outs: Part I, Simply-supported plates, J. Sound Vib., 54 (1977) 549–64.

    Article  Google Scholar 

  19. Rajamani, A. and Prabhakaran, R., Dynamic response of composite plates with cut-outs: Part II, Clamped-clamped plates, J. Sound Vib., 54 (1977) 565–76.

    Article  Google Scholar 

  20. Whitney, J. M., A study of the effects of coupling between bending and stretching on the mechanical behavior of layered anisotropic composite materials, Ph.D. Dissertation, The Ohio State University, Dept. of Engrg. Mech., 1968.

    Google Scholar 

  21. Whitney, J. M. and Leissa, A. W., Analysis of heterogeneous anisotropic plates, Trans. ASME, J. Appl. Mech., 36 (1969) 261–6.

    Article  Google Scholar 

  22. Leissa, A. W., Vibration of shells, NASA SP-288, Washington, DC, US Govt. Printing Off., 1973.

    Google Scholar 

  23. Leissa, A. W. and Kadi, A. S., Curvature effects on shallow shell vibrations, J. Sound Vib., 16(1971) 173–87.

    Google Scholar 

  24. Jones, R. M., Buckling and vibration of unsymmetrically laminated cross-ply rectangular plates, AIAA J., 11 (1973) 1626–32.

    Article  Google Scholar 

  25. Lin, C.-C. and King, W. W., Free transverse vibrations of rectangular unsymmetrically laminated plates, J. Sound Vib., 36 (1974) 91–103.

    Article  Google Scholar 

  26. Voigt, W., Observations on the problem of the transverse vibrations of rectangular plates (in German), Nachr. Ges. Wiss (Gottingen), 6 (1893) 225–30.

    Google Scholar 

  27. Ashton, J. E. and Anderson, J. D., The natural modes of vibration of boron-epoxy plates, Shock Vib. Bull., April (1969) 81–91.

    Google Scholar 

  28. Bert, C. W. and Mayberry, B. L., Free vibrations of unsymmetrically laminated composite plates with clamped edges, J. Composite Mat., 3 (1969) 282–93.

    Article  Google Scholar 

  29. Whitney, J. M., The effect of boundary conditions on the response of laminated composites, J. Composite Mat., 4 (1970) 192–203.

    Article  Google Scholar 

  30. Whitney, J. M. and Leissa, A. W., Analysis of a simply supported laminated anisotropic rectangular plate, AIAA J., 8 (1970) 28–33.

    Article  Google Scholar 

  31. Minich, M. D. and Chamis, C. C., Analytical displacements and vibrations of cantilevered unsymmetric fiber composite laminates, NASA Tech. Memo., NASA TMX-71699, 1975, 13 pp.

    Google Scholar 

  32. VON Kármán, T., Strength of materials problems in mechanical engineering (in German), Encyklopädie der Math. Wissenschaften, Bd.4 (1910) 311–85.

    Google Scholar 

  33. Bennett, J. A., Nonlinear vibration of simply supported angle ply laminated plates, AIAA J., 9 (1971) 1997–2003.

    Article  Google Scholar 

  34. Bennett, J. A., Some approximations in the nonlinear vibrations of unsymmetrically laminated plates, AIAA J., 10 (1972) 1145–6.

    Article  Google Scholar 

  35. Mayberry, B. L. and Bert, C. W., Experimental investigation of nonlinear vibrations of laminated anisotropic panels, Shock Vib. Bull., (1969) 191–9.

    Google Scholar 

  36. Bert, C. W., Nonlinear vibration of a rectangular plate arbitrarily laminated of anisotropic material, Trans. ASME, J. Appl. Mech., 40 (1973) 452–8.

    Article  Google Scholar 

  37. Chandra, R. and Basava Raju, B., Large deflection vibration of angle ply laminated plates, J. Sound Vib., 40 (1975) 393–408.

    Article  Google Scholar 

  38. Chandra, R. and Basava Raju, B., Large amplitude flexural vibration of cross ply laminated composite plates, Fibre Sci. Tech., 8 (1975) 243–63.

    Article  Google Scholar 

  39. Chandra, R., Large deflection vibration of cross-ply laminated plates with certain edge conditions, J. Sound Vib., 47 (1976) 509–14.

    Article  Google Scholar 

  40. Chia, C. Y. and Prabhakara, M. K., A general mode approach to nonlinear flexural vibrations of laminated rectangular plates, Trans. ASME, J. Appl. Mech., 45 (1978)623–8.

    Article  Google Scholar 

  41. Whitney, J. M. and Pagano, N. J., Shear deformation in heterogeneous anisotropic plates, Trans. ASME, J. Appl. Mech., 37 (1970) 1031–6.

    Article  Google Scholar 

  42. Noor, A. K., Free vibrations of multilayered composite plates, AIAA J., 11 (1973) 1038–9.

    Article  Google Scholar 

  43. Siu, C. C. and Bert, C. W., Sinusoidal response of composite-material plates with material damping, ASME Paper No.73-DET-120, 1973, 8 pp.

    Google Scholar 

  44. Clary, R. R., Vibration characteristics of unidirectional filamentary composite material panels, Composite Materials: Testing and Design (Second Conf.), ASTM STP497, 1972, pp. 415–38.

    Google Scholar 

  45. Srinivas, S., A refined analysis of thick anisotropic laminates, Indian Inst. Sci., Bangalore Aero. Engrng. Dept. Report, 1971, 68pp.

    Google Scholar 

  46. Srinivas, S. and Rao, A. K., Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates, Int. J. Solids Struc., 6(1910) 1463–81.

    Article  Google Scholar 

  47. Bert, C. W. and Chen, T. L. C., Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular plates, Int. J. Solids Struc., 14 (1978) 465–73.

    Article  Google Scholar 

  48. Hirashima, K., General higher-order equations of two-dimensional static and dynamic theories for homogeneous and laminated plates, Report, Princeton Univ., Dept. of Civil Engrng., July, 1980, 183 pp.

    Google Scholar 

  49. Mau, S.-T., Pian, T. H. H. and Tong, P., Vibration analysis of laminated plates and shells by a hybrid stress element, AIAA J., 11 (1973) 1450–2.

    Article  Google Scholar 

  50. Reddy, J. N., Free vibration of antisymmetric, angle-ply laminated plates including transverse shear deformation by the finite element method, J. Sound Vib., 66 (1979) 565–76.

    Article  Google Scholar 

  51. Reddy, J. N., A penalty plate-bending element for the analysis of laminated anisotropic composite plates, Int. J. Numer. Methods Engr., (1980).

    Google Scholar 

  52. Reddy, J. N., A comparison of closed-form and finite-element solutions of thick, laminated, anisotropic rectangular plates, School of Aerospace, Mechanical and Nuclear Engr., Univ. of Oklahoma (Norman), Report No.OU-AMNE-79-19, 1979, 39 pp.

    Google Scholar 

  53. Reddy, V. S., Analyses of cross-ply rectangular plates of bimodulus composite material, M.Sc. Thesis, Univ. of Oklahoma, 1980, 101 pp.

    Google Scholar 

  54. Bert, C. W., Reddy, J. N., Chao, W. C. and Reddy, V. S., Vibration of thick rectangular plates of bimodulus composite material, Off. Naval Res., Tech. Report No. 15, ContractN00014-78-C-0647, 1980, 26pp.

    Google Scholar 

  55. Wu, C. and Vinson, J. R., Nonlinear oscillations of laminated specially orthotropic plates with clamped and simply supported edges, J. Acoust. Soc. Amer.,49 (1971) 1561–7.

    Article  Google Scholar 

  56. Reddy, J. N. and Chao, W. C., Large deflection and large-amplitude free vibrations of laminated composite-material plates, School of Aerospace, Mechanical and Nuclear Engr., Univ. of Oklahoma, Report No.OU-AMNE-80-7, 1980, 25 pp.

    Google Scholar 

  57. Leissa, A. and Vagins, M., Stress optimization in nonhomogeneous materials, Developments in theoretical and applied mechanics, Proceedings of SECTAM 8,vol.8, 1976, pp. 13–22.

    Google Scholar 

  58. Leissa, A. W. and Vagins, M., The design of orthotropic materials for stress optimization, Int. J. Solids Struc, 14 (1978) 517–26.

    Article  Google Scholar 

  59. Whitney, J. M., Shear buckling of unsymmetrical cross-ply plates, J. Composite Mat., 3 (1969) 359–63.

    Article  Google Scholar 

  60. Ashton, J. E. and Love, T. S., Shear stability of laminated anisotropic plates, Composite materials: testing and design, ASTM STP460, 1969, pp. 352–61.

    Google Scholar 

  61. Ashton, J. E. and Love, T. S., Experimental study of the stability of composite plates, J. Composite Mat., 3 (1969) 230–42.

    Article  Google Scholar 

  62. Chamis, C. C., Buckling of anisotropic composite plates, Proc. ASCE, J. Struc. Div., 95 (1969) 2119–39.

    Google Scholar 

  63. Sarkisyan, V. S. and Movsisyan, L. A., A method for determining the critical loads on anisotropic plates, Soviet Engr. J. (Inzhenernyi Zhurnat), 5 (1965) 600–2.

    Google Scholar 

  64. Union Carbide Corporation, Case Western Reserve University and Bell Aerosystems Company, Integrated research on carbon composite materials, Air Force Materials Lab., Report AFML-TR-66-310, Part I (Oct. 1966), Part II (Dec. 1967), Part III (Jan. 1969), Part IV (Oct. 1969), Part V(1970).

    Google Scholar 

  65. Whitney, J. M., Bending, vibrations, and buckling of laminated anisotropic rectangular plates, Air Force Systems Command, Wright Patterson AFB, Ohio, Materials Lab. Report No. AFML-TR-70-75, Aug. 1970, 35 pp.

    Google Scholar 

  66. Whitney, J. M., Analysis of anisotropic rectangular plates, AIAA J., 10 (1972) 1344–5.

    Article  Google Scholar 

  67. Kicher, T. P. and Mandell, J. F., A study of the buckling of laminated composite plates, AIAA J., 9 (1971) 605–13.

    Article  Google Scholar 

  68. Mandel, J. F., An experimental study of the buckling of anisotropic plates, M.S. Thesis, Case Western Reserve University, 1968.

    Google Scholar 

  69. Viswanathan, A. V., Soong, T.-C. and Miller, R. E., JR., Buckling analysis for axially compressed flat plates, structural sections, and stiffened plates reinforced with laminated composites, NASA Contractor Report CR-1887, Nov. 1971, 75 pp.

    Google Scholar 

  70. Viswanathan, A. V., Soong, T.-C. and Miller, R. E., JR., Buckling analysis for structural sections and stiffened plates reinforced with laminated composites, Int. J. Solids Struc, 8 (1972) 347–67.

    Article  Google Scholar 

  71. Housner, J. M. and Stein, M., Numerical analysis and parametric studies of the buckling of composite orthotropic compression and shear panels, NASA TN D-7996, Oct. 1975, 102pp.

    Google Scholar 

  72. Chailleux, A., Hans, Y. and Verchery, G., Experimental study of the buckling of laminated composite columns and plates, Int. J. Mech. Sci., 17 (1975) 489–98.

    Article  Google Scholar 

  73. Sawyer, J. W., Flutter and buckling of general laminated plates, J. Aircraft, 14 (1977) 387–93.

    Article  Google Scholar 

  74. Chao, C. C., Koh, S. L. and Sun, C. T., Optimization of buckling and yield strengths of laminated composites (synoptic), AIAA J., 13(1975) 1131–2. Full paper available from NTIS as N75-19370, May 1974, 33 pp.

    Article  Google Scholar 

  75. Hayashi, T., Optimum design of cross-and angle-plied laminated composite plates under compression, Composite Mat. Struc. (Japan), 3 (1974) 18–20.

    Google Scholar 

  76. Schmit, L. A., JR. and Farshi, B., Optimum design of laminated fibre composite plates, Int. J. Numer. Methods Engr., 11 (1977) 623–40.

    Article  Google Scholar 

  77. Tsai, W. T., A theorem of stability of laminated plates, Trans. ASME, J. Appl. Mech., 42 (1975) 237–9.

    Article  Google Scholar 

  78. Agarwal, B. and Davis, R. C., Minimum-weight designs for hat-stiffened composite panels under uniaxial compression, NASA TN D-7779, Nov. 1974, 44 pp.

    Google Scholar 

  79. Stroud, W. J. and Agranoff, N., Minimum-mass design of filamentary composite panels under combined loads: design procedure based on simplified buckling equations, NASA TN D-8257, Oct. 1976, 51 pp.

    Google Scholar 

  80. Stroud, W. J., Agranoff, N. and Anderson, M.S., Minimum-mass design of filamentary composite panels under combined loads: design procedure based on a rigorous buckling analysis, NASA TN D-8417, July 1977, 40 pp.

    Google Scholar 

  81. Williams, J. G. and Mikulas, M. M., JR., Analytical and experimental study of structurally efficient composite hat-stiffened panels loaded in axial compression, NASA TM X-72813, Jan. 1976, 21 pp.

    Google Scholar 

  82. Williams, J. G. and Stein, M., Buckling behavior and structural efficiency of open-section stiffened composite compression panels, AIAA J., 14 (1976) 1618–26.

    Article  Google Scholar 

  83. Whitney, J. M., The effect of transverse shear deformation on the bending of laminated plates, J. Composite Mat., 3 (1969) 534–47.

    Article  Google Scholar 

  84. Vinson, J. R. and Smith, A. P., JR., The effect of transverse shear deformation on the elastic stability of plates of composite materials, AFOSR TR-75-1628, March 1975, 77 pp.

    Google Scholar 

  85. Turvey, G. J., Biaxial buckling of moderately thick laminated plates, J. Strain Analysis, 12 (1977) 89–96.

    Article  Google Scholar 

  86. Ashton, J. E., Analysis of anisotropic plates II, J. Composite Mat., 3 (1969) 470–9.

    Article  Google Scholar 

  87. Morgan, H. S. and Jones, R. M., Buckling of rectangular cross-ply laminated plates with nonlinear stress-strain behavior, Trans. ASME, J. Appl. Mech., 46 (1979) 637–43.

    Article  Google Scholar 

  88. Flaggs, D. L. and Vinson, J. R., Elastic stability of generally laminated composite plates including hygrothermal effects, AFOSR TR 78-1349, July 1977,68 pp.

    Google Scholar 

  89. Bauld, N. R., JR. and Satyamurthy, K., Collapse load analysis for plates and panels, Air Force Flight Dynamics Lab., Wright Patterson AFB, Ohio, AFFDL-TR-79-3038, May 1979, 209 pp.

    Google Scholar 

  90. Meffert, B., Derek, H. and Menges, G., Stress deformation behavior of orthotropic plates with initial curvature made of glass fiber-reinforced unsaturated polyester plastics (GFUP) under uniaxial load in the plane of the plate (in German), Bauingenieur, 52 (1977) 211–16.

    Google Scholar 

  91. Stroud, W. J., Anderson, M. S. and Hennessy, K. W., Effect of bow-type initial imperfection on the buckling load and mass of graphite-epoxy blade-stiffened panels, NASA Tech. Memo., NASATM-74063, 1977, 25 pp.

    Google Scholar 

  92. Montforton, G. R., Discrete element finite displacement analysis of anisotropic sandwich shells, Ph.D. hesis, Case Western Reserve Univ., Cleveland, Ohio, 1970.

    Google Scholar 

  93. Schmit, L. A., JR. and Montforton, G. R., Finite deflection discrete element analysis of sandwich plates and cylindrical shells with laminated faces, AIAA J., 8 (1970) 1454–61.

    Article  Google Scholar 

  94. Chan, D. P., An analytical study of the post buckling of laminated, anisotropic plates, Ph.D. Thesis, Case Western Reserve Univ., Cleveland, Ohio, 1971.

    Google Scholar 

  95. Islam, M. R., Buckling and postbuckling strength of anisotropic plates, Ph.D. Thesis, Case Western Reserve Univ., Cleveland, Ohio, 1971.

    Google Scholar 

  96. Nara, H. R. (Ed.), Interface and mechanics research in fiber reinforced composites, Air Force Materials Lab., Wright Patterson AFB, Ohio, Tech. Report. AFML-TR-71-260, March 1972, 262 pp.

    Google Scholar 

  97. Turvey, G. J., A contribution to the elastic stability of thin-walled structures fabricated from isotropic and orthotropic materials, Ph.D. Thesis, Dept. of Civil Engr., Univ. of Birmingham, 1971.

    Google Scholar 

  98. Turvey, G. J. and Wittrick, W. H., The large deflection and postbuckling behavior of some laminated plates, Aero. Quart., 24 (1973) 77–86.

    Google Scholar 

  99. Harris, G. Z., The buckling and post-buckling behavior of composite plates under biaxial loading, Int. J. Mech. Sci., 17 (1975) 187–202.

    Article  Google Scholar 

  100. Chandra, R., Postbuckling analysis of crossply laminated plates, AIAA J., 13 (1975) 1388–9.

    Article  Google Scholar 

  101. Chia, C. Y. and Prabhakara, M. K., Postbuckling behavior of unsymmetrically layered anisotropic rectangular plates, J. Appl. Mech., 41 (1974) 155–62.

    Article  Google Scholar 

  102. Prabhakara, M. K., Post-buckling behaviour of simply-supported cross-ply rectangular plates, Aero. Quart., 27 (1976) 309–16.

    Google Scholar 

  103. Noor, A. K., Mather, M. D. and Anderson, M. S., Exploiting symmetries for efficient postbuckling analysis of composite plates, AIAA J., 15 (1977) 24–32.

    Article  Google Scholar 

  104. Ter-emmanuil’yan, N. YA., Stability of an orthotropic flexible square plate weakened by a square opening, Polymer Mech., 7 (1971) 425–9.

    Article  Google Scholar 

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Leissa, A.W. (1981). Advances in Vibration, Buckling and Postbuckling Studies on Composite Plates. In: Marshall, I.H. (eds) Composite Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8120-1_21

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  • DOI: https://doi.org/10.1007/978-94-009-8120-1_21

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