In this paper, variationally consistent layer-wise trigonometric shear deformation theory has been extended to deal with free vibration of two-layered laminated cross-ply plates. Governing differential equations are derived by making use of a displacement field which allows a sinusoidal variation of the in-plane displacements through the laminate thickness. In this displacement based theory, constitutive relations between shear-stress and shear-strains are satisfied in both the layers, and, therefore, shear correction factor is not required. Compatibility at the layer interface in respect of in-plane displacement and compatibility in respect of transverse shear-stress is satisfied, yet present theory contains fewer unknown variables than that of the first order shear deformation theory. Effects of rotary inertia and other inertias are also included. Efficacy of the present theory is demonstrated through illustrative examples.
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References
1.
1. Hanna, N.F. and Leissa, A.W. (1994). A Higher Order Shear Deformation Theory for the Vibration of Thick Plates , Journal of Sound and Vibration, 170(4): 545–555 .
2.
2. Kant, T. and Menon, M.P. (1993). A Finite Element-Difference Computational Model for Stress Analysis of Layered Composite Cylindrical Shells , Finite Element Analysis and Design, 14: 55–71 .
3.
3. Noor, A.K., Burton, W.S. and Peters, M. (1990). Predictor-Corrector Procedures for Free Vibration Analyses of Multilayered Composite Plates and Shells , Computer Methods in Applied Mechanics and Engineering, 82: 341–361 .
4.
4. Reddy, J.N. (1989). On the Generalization of Displacement-Based Laminate Theories , Applied Mechanics Reviews, 42: S213–S222 .
5.
5. Kapania, R.K. and Raciti, S. (1989). Recent Advances in Analysis of Laminated Beams and Plates, Part-I: Shear Effects and Buckling , AIAA Journal, 27: 923–934 .
6.
6. Kapania, R.K. and Raciti, S. (1989). Recent Advances in Analysis of Laminated Beams and Plates, Part-II: Vibration and Wave Propagation , AIAA Journal, 27: 935–946 .
7.
7. Reddy, J.N. and Robbins, Jr., D.H. (1994). Theories and Computational Models for Composite Laminates . Applied Mechanics Reviews, 47: 147–169 .
8.
8. Reddy, J.N. (1989). On Refined Computational Models of Composite Laminates , International Journal for Numerical Methods in Engineering, 27: 361–382 .
9.
9. Reddy, J.N. (1990). A Review of Refined Theories of Laminated Composite Plates , Shock and Vibration Digest, 22: 3–17 .
10.
10. Bert, C.W. and Francis, P.H. (1974). Composite Material Mechanics: Structural Mechanics , AIAA Journal, 12: 1173–1186 .
11.
11. Mallikarjuna and Kant, T. (1993). A Critical Review and Some Results of Recently Developed Refined Theories of Fiber-Reinforced Laminated Composites and Sandwiches , Composite Structures, 23: 293–312 .
12.
12. Liew, K.M., Xiang, Y. and Kitipornchai, S. (1995). Research on Thick Plate Vibration: A Literature Survey , Journal of Sound and Vibration, 180(1): 163–176 .
13.
13. Noor, A.K. and Burton, W.S. (1989). Assessment of Shear Deformation Theories for Multilayered Composite Plates , Applied Mechanics Reviews, 42: 1–13 .
14.
14. Noor, A.K. and Burton, W.S. (1989). Stress and Free Vibration Analysis of Multilayered Composite Plates , Composite Structures, 11: 183–204 .
15.
15. Reddy, J.N. (1997). Mechanics of Laminated Composite Plates: Theory and Analysis, pp. 782, CRC Press, Inc., Boca Raton, Florida, USA .
16.
16. Reddy, J.N. (1993). An Evaluation of Equivalent-single-layer and Layerwise Theories of Composite Laminates, 25: 21–35 .
17.
17. Bose, P. and Reddy, J.N. (1998). Analysis of Composite Plates Using Various Plate Theories Part 1: Formulation and Analytical Solutions , Structural Engineering and Mechanics, 6: 583–612 .
18.
18. Bose, P. and Reddy, J.N. (1998). Analysis of Composite Plates Using Various Plate Theories Part 2: Finite Element Model and Numerical Results , Structural Engineering and Mechanics, 6: 727–746 .
19.
19. Whitney, J.M. (1969). The Effect of Transverse Shear Deformation on the Bending of Laminated Plates , Journal of Composite Materials, 3: 534–547 .
20.
20. Srinivas, S. (1973). A Refined Analysis of Composite Laminates , Journal of Sound and Vibration, 30: 495–507 .
21.
21. Ren, J.G. (1986). A New Theory of Laminated Plate , Composite Science and Technology, 26: 225–239 .
22.
22. DiSciuva, M. (1992). Multilayered Anisotropic Plate Models with Continuous Interlaminar Stresses , Composite Structures, 22: 149–167 .
23.
23. Cho, M. and Parmerter, R.R. (1992). An Efficient Higher Order Plate Theory for Laminated Composites , Composite Structures, 20: 113–123 .
24.
24. Shimpi, R.P. and Ghugal, Y.M. (2000). A Layerwise Shear Deformation Theory for Two Layered Cross-Ply Laminated Plates, 7: 331–353 .
25.
25. Jones, R.M. (1975). Mechanics of Composite Materials, pp. 31–56, McGraw-Hill, New York .
26.
26. Szilard, R. (1974). Theory and Analysis of Plates, Classical and Numerical Methods. Englewood Cliffs, Prentice-Hall Inc., New Jersey .
27.
27. Pister, K.S. and Dong, S.B. (1959). Elastic Bending of Layered Plates , ASCE Journal of the Engineering Mechanics Division, 85: 1–10 .
28.
28. Noor, A.K. (1973). Free Vibrations of Multilayered Composite Plates , AIAA Journal, 11(7): 1038–1039 .
29.
29. Nosier, A., Kapania, R.K. and Reddy, J.N. (1993). Free Vibration Analysis of Laminated Plates Using a Layerwise Theory , AIAA Journal, 31(12): 2335–2346 .
30.
30. Cho, K.N., Bert, C.W. and Striz, A.G. (1991). Free Vibrations of Laminated Rectangular Plates Analyzed by Higher Order Individual-layer Theory , Journal of Sound and Vibration, 145(3): 429–442 .
31.
31. 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: 157–170 .
32.
32. Bhaskar, K. and Varadan, T.K. (1992). Comments on Free Vibrations of Laminated Rectangular Plates Analyzed by Higher Order Individual-layer Theory , Journal of Sound and Vibration, 154(1): 178–179 .
