Local and Global Damped Vibrations of Plates with a Viscoelastic Soft Flexible Core: An Improved High-order Approach

Abstract

An improved high-order theory is presented to investigate the dynamic behavior of thin and thick fiber-reinforced plastic (FRP) plates with a soft viscoelastic flexible core. Shear deformation theory is used for the face sheets while three-dimensional elasticity theory is used for the soft core. The analysis permits nonlinear distortions of the cross-sectional plane of the core as well as changes in its height. The analysis determines the damped natural frequencies, loss factors, and local and global mode shapes of plates. Some of the results are hitherto not reported in the literature based on a higher-order plate theory (HSAPT). Transverse shear and rotary inertia effects of face sheets are taken into consideration. For simply supported boundary condition, closed-form solutions are obtained by Navier’s technique. Numerical results are presented and compared with the experimental and theoretical results found in literature.

Keywords

plates viscoelastic damping vibrations soft flexible core higher order

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References

Allen, H.G. (1969). Analysis and Design of Structural Plates, Chapter 9-10, Pergamon, London .

Plantema, F.J. (1966). Construction, John Wiley, New York .

Zenkert, D. (1995). An Introduction to Construction, Chapters 3, 4 and 12, Chameleon Press Ltd, London .

Reddy, J.N. (1997). Mechanics of Laminated Composite Plates, Theory and Analysis, Chapter 5, CRC Press, Boca Raton, FL .

Frostig, Y. , Baruch, M. , Vilnay, O. and Sheinman, I. (1992). High-Order Theory for Beam Behavior with Transversely Flexible Core , Journal of Engineering Mechanics, 118(5): 1026-1043 .

Frostig, Y. and Baruch, M. (1994). Free Vibrations of Beams with a Transversely Flexible Core: A High order Approach , Journal of Sound and Vibration, 176(2): 195-208 .

Frostig, Y. (1998). Buckling of Plates with a Flexible Core: High-order Theory , Int. J. Solids Structures, 35(3-4): 183-204 .

Sokolinsky, V. , Steven, R. and Frostig, Y. (2000). Boundary Condition Effects in Free Vibrations of Higher-order Soft Beams , AIAA Journal, 40(6): 1220-1227 .

Thomsen, O.T. and Frostig, Y. (1997). Local Effects in Plates: Photoelastic Investigation Versus High-order Theory , J. Composite Structures, 37(1): 97-108 .

10.

Swanson, S.R. and Kim, J. (2000). Comparison of a Higher order Theory for Beams with Finite Element and Elasticity Analyses , Journal of Structures and Materials, 2(1): 33-49 .

11.

Meunier, M. and Shenoi, R.A. (1999). Free Vibration Analysis of Composite Plates , J. Mech. Eng. Sci., Part C, 213: 715-727 .

12.

Meunier, M. (2001). Dynamic Analysis of Composite Plates Using Higher order Theory, PhD Thesis, University of Southampton.

13.

Meunier, M. and Shenoi, R.A. (2001). Dynamic Analysis of Composite Plates with Damping Model using High-order Shear Deformation Theory , J. Composite Structures, 54: 243-254 .

14.

Nayak, A.K. , Moy, S.S.J. and Shenoi, R.A. (2002). Free Vibration Analysis of Composite Plates Based on Higher-order Theory , Composites: Part B, 33: 505-519 .

15.

Raville, M.E. and Ueng, C.E.S. (1967). Determination of Natural Frequencies of Vibration of a Plate , Exp. Mech., 7: 490-493 .

16.

Chandra, R. , Singh, S.P. and Gupta, K. (1999). Damping Studies in Fiber-Reinforced Composites - A Review , J. Composite Structures, 46(1): 41-51 .

17.

Noor, A.K. , Burton, W.S. and Bert, C.W. (1996). Computational Models for Plates and Shells , Applied Mechanics Rev., 49(3): 155-199 .

18.

Adam, R.D. and Bacon, D.G. (1973). Effect of Fiber Orientation and Laminate Geometry on the Dynamic Properties of CFRP , J. Composite Mater., 7: 402-428 .

19.

Ni, R.G. , Lin, D.X. and Adams, R.D. (1984). The Dynamic Properties of Carbon Glass Fiber Laminated Composites: Theoretical , Experimental and Economic Considerations, Composite, 15(4): 297-304 .

20.

Alam, N. and Asnani, N.T. (1986) Vibration and Damping Analysis of Fibre-reinforced Composite Material Plates , J. Compos. Mater., 20(2): 2-18 .

21.

Rikards, Chate (1993). Analysis and Optimal Design of Damping Properties of Laminated Composites , In: Proceedings of The 9th International Conference on Composite Materials (ICCM/9), Madrid, pp. 329-336 .

22.

Crane, G. (1992). Analytical Model for Prediction of the Damping Loss Factor of Composite Materials , Polym. Compos., 13(3): 127-132 .

23.

Cupial, P. and Niziol, J. (1995). Vibration and Damping Analysis of a Three Layered Composite Plate with a Viscoelastic Mid-layer , J. Sound Vibr., 183(1): 99-114 .

24.

Lin, D.X. , Ni, R.G. and Adams, R.D. (1984). Prediction and Measurement of The Vibrational Damping Parameters of Carbon and Glass Fiber Reinforced Plastic Plates , J. Composite Mater., 18: 132-152 .

25.

Bicos, A. and Springer, G. (1989). Analysis of Free Damped Vibrations of Laminated Composite Plates and Shells , Int. J. Solids Structr., 25(2): 129-149 .

26.

Hashin, Z. (1970). Complex Moduli of Viscoelastic Composites: II. Fiber Reinforced Materials , Int. J. Solids Structr., 6: 797-807 .

27.

Nayak, A.K. , Shenoi, R.A. and Moy, S.S.J. (2002). Analysis of Damped Composite Plates Using Plate Bending Elements with Substitute Shear Strain Fields based on Reddy’s Higher-order Theory , Int. J. Mech. Engrs., Part C, 216: 591-606 .