Higher-order closed-form solutions for free vibration of laminated composite and sandwich shells

Journal of Sandwich Structures and Materials

Volumn 8, Issue 2, 2006, Pages 95-124

  Garg, Ajay Kumar ^a   Khare, Rakesh Kumar ^b   Kant, Tarun ^c  

^a Government Engineering College Bilaspur   (India)

^b SHRI G S INSTITUTE OF TECHNOLOGY AND SCIENCE   (India)

^c INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

Author keywords

Composite and sandwich laminates; Cross ply laminates; Free vibration; Higher order shear deformation theory; Plates and shells

Indexed keywords

EID: 33646691468     PISSN: 10996362     EISSN: 15307972     Source Type: Journal    
DOI: 10.1177/1099636206058779     Document Type: Article

References (36)

1. Reissner, E. (1945). The Effect of Transverse Shear Deformation on the Bending of Elastic Plates, ASME Journal of Applied Mechanics, 12 (2). 69-77.
2. Mindlin, R.D. (1951). Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic Elastic Plates, ASME Journal of Applied Mechanics, 18: 31-38.
3. Yang, P.C., Norris, C.H. and Stavsky, Y. (1966). Elastic Wave Propagation in Heterogeneous Plates, International Journal of Solids and Structures, 2: 665-684.
4. Reissner, E. (1985). Reflection on the Theory of Elastic Plates, Applied Mechanics Review, 38: 1453-1464.
5. Noor, A.K. and Burton, W.S. (1989). Refinement of Higher-order Laminated Plate Theories, Applied Mechanics Review, 42: 1-13.
6. Reddy, J.N. (1990). A Review of Refined Theories of Laminated Composite Plates, Shock and Vibration Digest, 22: 3-17.
7. Noor, A.K. (1973). Free Vibration of Multilayered Composite Plates, AIAA Journal, 11: 1038-1039.
8. Bert, C.W. and Chen, T.L.C. (1978). Effect of Shear Deformation on Vibration of Antisymmetric Angle-ply Laminated Rectangular Plates, International Journal of Solids and Structures, 14: 465-473.
9. Reddy, J.N. (1979). Free Vibration of Antisymmetric, Angle-ply Laminated Plates Including Transverse Shear Deformation by the Finite Element Method, Journal of Sound and Vibration, 66 (4). 565-576.
10. Reddy, J.N. (1984). Exact Solutions of Moderately Thick Laminated Shells, Journal of Engineering Mechanics, 110 (5). 794-809.
11. Sanders, Jr., J.L. (1959). An Improved First Approximation Theory for Thin Shells, NASA Technical Report, R-24.
12. Nosier, A. and Reddy, J.N. (1992). Vibration and Stability Analyses of Cross-ply Laminated Circular Cylindrical Shells, Journal of Sound and Vibration, 157 (1). 139-159.
13. Kant, T., Owen, D.R.J. and Zienkiewicz, O.C. (1982). A Refined Higher Order C0 Plate Bending Element, Computers & Structures, 15: 177-183.
14. Reddy, J.N. (1984). A Simple Higher-order Theory for Laminated Composites, ASME Journal of Applied Mechanics, 51: 745-752.
15. Reddy, J.N. and Phan, N.D. (1985). Stability and Vibration of Isotropic, Orthotropic and Laminated Plates According to a Higher-order Shear Deformation Theory, Journal of Sound and Vibration, 98 (2). 157-170.
16. Khdeir, A.A. (1988). Free Vibration and Buckling of Symmetric Cross-ply Laminated Plates by an Exact Method, Journal of Sound and Vibration, 126 (3). 447-461.
17. Khdeir, A.A. (1989). Free Vibration and Buckling of Unsymmetric Cross-ply Laminated Plates Using a Refined Theory, Journal of Sound and Vibration, 128 (3). 377-395.
18. Kant, T. and Mallikarjuna (1989). Vibrations of Unsymmetrically Laminated Plates Analyzed by Using a Higher Order Theory with a C0 Finite Element Formulation, Journal of Sound and Vibration, 134: 1-16.
19. Bhimaraddi, A. (1984). A Higher Order Theory for Free Vibration Analysis of Circular Cylindrical Shells, International Journal of Solids and Structures, 20 (7). 623-630.
20. Liew, K.M. and Lim, C.W. (1996). A Higher-order Theory for Vibration of Doubly Curved Shallow Shells, ASME Journal of Applied Mechanics, 63: 587-593.
21. Reddy, J.N. and Khdeir, A.A. (1989). Buckling and Vibration of Laminated Composite Plates Using Various Plate Theories, AIAA Journal, 27 (12). 1808-1817.
22. Matsunaga, H. (2000). Vibration and Stability of Cross-ply Laminated Composite Plates According to a Global Higher-order Plate Theory, Composite Structures, 48: 231-244.
23. Kant, T. and Swaminathan, K. (2001). Analytical Solutions for Free Vibration of Laminated Composite and Sandwich Plates Based on a Higher-order Refined Theory, Composite Structures, 53: 73-85.
24. Pandya, B.N. and Kant, T. (1988). Finite Element Stress Analysis of Laminated Composite Plates Using Higher Order Displacement Model, Composite Science Technology, 32: 137-155.
25. Kant, T. and Manjunatha, B.S. (1988). An Unsymmetric FRC Laminate C0 Finite Element Model with 12 Degrees of Freedom Per Node, Engineering Computation, 5 (3). 300-308.
26. Singh, B.N., Yadav, D. and Iyengar, N.G.R. (2001). Natural Frequencies of Composite Plates with Random Material Properties Using Higher-order Shear Deformation Theory, International Journal of Mechanical Science, 43: 2193-2214.
27. Ganapathi, M., Patel, B.P., Pawargi, D.S. and Patel, H.G. (2002). Comparative Dynamic Studies of Thick Laminated Composite Shells Based on Higher-order Theories, Structural Engineering and Mechanics, 13 (6). 695-711.
28. Kabir, H.R.H., Al-Khaleefi, A.M. and Chaudhuri, R.A. (2003). Frequency Response of a Moderately Thick Antisymmetric Cross-ply Cylindrical Panel Using Mixed Type of Fourier Solution Functions, Journal of Sound and Vibration, 259 (4). 809-828.
29. Khare, R.K., Kant, T. and Garg, A.K. (2003). Closed-form Thermo-mechanical Solution of Higher-order Theories of Cross-ply Laminated Shallow Shells, Composite Structures, 59: 313-340.
30. Liew, K.M., Peng, L.X. and Ng, T.Y. (2002). Three-dimensional Vibration Analysis of Spherical Shell Panels Subjected to Different Boundary Conditions, International Journal of Mechanical Science, 44: 2103-2117.
31. Zhang, J.Z., Ng, T.Y. and Liew, K.M. (2003). Three-dimensional Theory of Elasticity for Free Vibration Analysis of Composite Laminates via Layerwise Differential Quadrature Modelling, International Journal Numerical Methods in Engineering, 57: 1819-1844.
32. Liew, K.M., Lim, C.W. and Kitipornchai, S. (1997). Vibration of Shallow Shells: A Review with Bibliography, Applied Mechanics Review, 50 (8). 431-444.
33. Qatu, M.S. (2002). Recent Research Advances in the Dynamic Behavior of Shells: 1989-2000, Part 1: Laminated Composite Shells, Applied Mechanics Review, 55 (4). 325-350.
34. Qatu, M.S. (2002). Recent Research Advances in the Dynamic Behavior of Shells: 1989-2000, Part 2: Homogeneous Shells, Applied Mechanics Review, 55 (5). 415-434.
35. Cook, R.D., Malkus, D.S., Plesha, M.E. and Witt, R.J. (2000). Concepts and Applications of Finite Element Analysis, John Wiley and Sons, New York.
36. Raville, M.E. and Veng, C.E.S. (1967). Determination of Natural Frequencies of Vibration of Sandwich Plates, Experimental Mechanics, 7: 490-493.