The parametric resonance characteristics of laminated composite doubly curved panels subjected to various in-plane static and periodic compressive edge loadings, including partial and concentrated edge loading are studied using finite element analysis. The first order shear deformation theory is used to model the doubly curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to the Sander’s first approximation for doubly curved laminated shells, which can be reduced to Love’s and Donnell’s theories by means of tracers. The effects of number of layers, static load factor, side to thickness ratio, shallowness ratio, boundary conditions, degree of orthotropy, ply orientations and various load parameters on the principal instability regions of doubly curved panels are studied in detail using Bolotin’s method. Quantitative results are presented to show the effects of shell geometry, lamination details and load parameters on the stability boundaries. Results of plates and cylindrical shells are also presented as special cases and are compared with those available in the literature.
1. Evan-Iwanowski, R. M.1965. “On the parametric response of structures,”Applied Mechanics Review, 18: 699-702.
2.
2. Srinivasan, R. S. and P. Chellapandi. 1986. “Dynamic stability of rectangular laminated composite plates,”Computers and Structures, 24(2): 233-238.
3.
3. Chen, L. W. and J. Y. Yang. 1990. “Dynamic stability of laminated composite plates by the finite element method,”Computers and Structures, 36(5): 845-851.
4.
4. Kwon, Y. W.1991. “Finite element analysis of dynamic instability of layered composite plates using a high order bending theory,”Computers and Structures, 38(1): 57-62.
5.
5. Bolotin, V. V.1964. The Dynamic Stability of Elastic System, San Francisco: Holden-Day.
6.
6. Yao, J. C.1965. “Nonlinear elastic buckling and parametric excitation of a cylinder under axial loads,”Journal of Applied Mechanics, 32: 109-115.
7.
7. Bert, C. W. and V. Birman. 1988. “Parametric instability of thick orthotropic circular cylindrical shells,”Acta Mechanica, 71: 61-76.
8.
8. Cederbaum, G.1992. “Analysis of parametrically excited laminated shells,”International Journal of Mechanical Sciences, 34: 241-250.
9.
9. Argento, A. and R. A. Scott. 1993. “Dynamic instability of layered anisotropic circular cylindrical shells, part I: theoretical development,”Journal of Sound and Vibration, 162: 311-322.
10.
10. Argento, A. and R. A. Scott. 1993. “Dynamic instability of layered anisotropic circular cylindrical shells, part II: numerical results,”Journal of Sound and Vibration, 162: 323-332.
11.
11. Argento, A. and R. A. Scott. 1993. “Dynamic instability of a composite circular cylindrical shell subjected to combined axial and torsional loading,”Journal of Composite Materials, 27: 1722-1738.
12.
12. Ganapathi, M. and V. Balamurugan. 1998. “Dynamic instability analysis of a laminated composite circular cylindrical shell,”Computers and Structures, 69: 181-189.
13.
13. Ng, T. Y., K. Y. Lam and J. N. Reddy. 1998. “Dynamic stability of cross-ply laminated composite cylindrical shells,”International Journal of Mechanical Sciences, 40(8): 805-823.
14.
14. Ganapathi, M., B. P. Patel and C. T. Sambandam. 1999. “Parametric dynamic instability analysis of laminated composite conical shells,”Journal of Reinforced Plastics and Composites, 18(14): 1336-1346.
15.
15. Chaudhuri, R. A. and K. R. Abuarja. 1988. “Extract solution of shear flexible doubly curved antisymmetric angle ply shells,”International Journal of Engineering Sciences, 26(6): 587-604.
16.
16. Reddy, J. N.1984. “Exact solutions of moderately thick laminated shells,”Journal of Engineering Mechanics, ASCE, 110: 794-809.
17.
17. Chandrashekhara, K.1989. “Free vibrations of anisotropic laminated doubly curved shells,”Computers and Structures, 33: 435-440.
18.
18. Qatu, M. S. and A. W. Leissa. 1991. “Natural frequencies for cantilevered doubly curved laminated composite shallow shells,”Composite Structures, 17: 227-255.
19.
19. Singh, A. V. and V. Kumar. 1998. “On free vibrations of fiber reinforced doubly curved panels, Part 2: Applications,”ASME Journal of Vibration and Acoustics, 120(1): 295-300.
20.
20. Qatu, M. S.1992. “Review of shallow shell vibration research,”Shock and Vibration Digest, 24, 3-15.
21.
21. Liew, K. M., C. W. Lim and S. Kitipornchai. 1997. “Vibration of shallow shells: a review with bibliography,”Applied Mechanics Review, 50: 431-444.
22.
22. Baharlou, B. and A. W. Leissa. 1987. “Vibration and buckling of generally laminated composite plates with arbitary edge conditions,”International Journal of Mechanical Sciences, 29(8), 545-555.
23.
23. Ye, J. and K. P. Soldatos. 1995. “Three dimensional buckling analysis of laminated composite hollow cylinders and cylindrical panels,”International Journal of Solids and Structures, 32(13): 1949-1962.
24.
24. Moita, J. S., C. M. M. Soares and C. A. M. Soares. 1999. “Buckling and dynamic behaviour of laminated composite structures using a discrete higher order displacement model,”Computers and Structures, 73: 407-423.
25.
25. Matsunaga, H.1999. “Vibration and stability of thick simply supported shallow shells subjected to in-plane stresses,”Journal of Sound and Vibration, 225: 41-60.
26.
26. Leissa, A. W. and E. F. Ayub. 1988. “Vibration and buckling of simply supported rectangular plate subjected to a pair of in-plane concentrated forces,”Journal of Sound and Vibration, 127: 155-171.
27.
27. Leissa, A. W. and E. F. Ayub. 1989. “Tension buckling of rectangular sheets due to concentrated forces,”Journal of Engineering Mechanics, ASCE,115: 2749-2762.
28.
28. Libai, A. and D. Durban. 1977. “Buckling of cylindrical shells subjected to non-uniform axial loads,”Journal of Applied Mechanics, 44: 714-720.
29.
29. Durban, D. and E. Ore. 1999. “Plastic buckling of circular cylindrical shells under non-uniform axial loads,”ASME Journal of Applied Mechanics, 66: 374-379.
30.
30. Ganapathi, M., T. K. Varadan and V. Balamurugan. 1994. “Dynamic stability of laminated composite curved panels using finite element method,”Computers and Structures, 53(2): 335-342.
31.
31. Moorthy, J., J. N. Reddy and R. H. Plaut. 1990. “Parametric instability of laminated composite plates with transverse shear deformation,”International Journals of Solids Structures, 26: 801-811.
32.
32. Ganapathi, M., P. Boisse and D. Solaut. 1999. “Non-linear dynamic stability analysis of composite laminates under periodic in-plane loads,”International Journal for Numerical Methods in Engineering, 46: 943-956.
33.
33. Chakraborty, D., J. N. Bandyopadhyay and P. K. Sinha. 1996. “Finite element free vibration analysis of doubly curved laminated composite shells,”Journal of Sound and Vibration, 191: 491-504.
34.
34. Narita, Y. and X. Zhao. 1998. “An optimal design for the maximum fundamental frequency of laminated shallow shells,”International Journal of Solids and Structures, 35(20): 2571-2583.
