Dynamic Response of In-plane Pre-stressed Sandwich Panels with a Viscoelastic Flexible Core and Different Boundary Conditions

Abstract

A new mathematical method and double Fourier series set of functions is developed to find out the local and global transverse and in-plane mode shapes, damped natural frequencies and modal loss factors in composite sandwich panels with multilayered laminated face sheets, viscoelastic flexible core and arbitrary boundary conditions. An improved high order sandwich plate theory (IHSAPT) is applied to investigate the dynamic behavior of fiber reinforced plastic (FRP) sandwich thin and thick panels. The present analysis is very general and valid for any type of core, any type of boundary conditions as well as for the cases where the conditions at the upper face sheet are different from those at the lower one along the same edge. Interaction between static in-plane initial stress and dynamic response of a sandwich panel are studied in this article. For different boundary conditions, solutions are obtained using the simple proposed identical double Fourier series functions and Stokes’s transformation technique. The effect of some parameters such as panel aspect ratio, thickness of core-thickness of panel ratio, and initial in-plane stresses on dynamic response of composite sandwich panel are discussed and studied in detail.

Keywords

sandwich panels Stokes’s transformation viscoelastic flexible core damping in-plane pre-stress

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References

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

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

Zenkert, D. (1995). An Introduction to Sandwich Construction, UK, Chameleon Press LTD, London , Chap. 3, 4 and 12.

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

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

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

Frostig, Y. (1998). Buckling of Sandwich 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 Sandwich Beams , AIAA Journal, 40(6): 1220-1227 .

Thomsen, O. T. and Frostig, Y. (1997). Local Effects in Sandwich 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 Sandwich Beams With Finite Element and Elasticity Analyses , Journal of Sandwich Structures and Materials, 2(1): 33-49 .

11.

Meunier, M. and Shenoi, R. A. (2000). Free Vibration Analysis of Composite Sandwich Plates , J. Mech Eng Sci. Part C, 213(7): 715-727 .

12.

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

13.

Meunier, M. and Shenoi, R. A. (2001). Dynamic Analysis of Composite Sandwich Plates With Damping Modeled Using High-order Shear Deformation Theory , J. Composite Structures, 54(2-3): 243-254 .

14.

Nayak, A. K. and Shenoi, R. A. (2002). Free Vibration Analysis of Composite Sandwich Plates Based on Higher-order Theory , J. Composites: Part B, 33(4): 505-519 .

15.

Raville, M. E. and Ueng, C. E. S. (1967). Determination of Natural Frequencies of Vibration of a Sandwich Plate , J. Exp. Mech., 7(4): 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 Sandwich 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 Geometrry on the Dynamic Properties of CFRP , J. Composite Mater., 7(3): 402-428 .

19.

Ni, R. G. , Lin, D. X. and Adams, R. D. (1984). The Dynamic Properties of Carbon Glass Fiber Sandwich Laminates Composites. Exp. Econ. Considerations , J. Composite, 15(4): 297-304 .

20.

Alam, N. and Asnani, N. T. (1986). Vibration and Damping Analysis of Fiber-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, 16 July, 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(2): 132-152 .

25.

Bicos, A. and Springer, G. (1989). Analysis of Free Damped Vibrations of Laminated Composite Plates And Shell , Int. J. Solid Struct., 25(2): 129-149 .

26.

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

27.

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

28.

Sun, C. T. and Chattopadhyay, S. (1975). Dynamic Response of Anisotropic Laminated Plate Under Initial Stress to Impact of a Mass ., J. Appl. Mech., 42(5): 693-698 .

29.

Whitney, M. and Pagano, N. J. (1970). Shear Deformation in Heterogeneous Anisotropic Plates , J. Appl. Mech., 37(8): 1031-1036 .

30.

Dobyns, A. L. (1980). Analysis of Simply Supported Orthotropic Plates Subjected to Static and Dynamic Load , J. AIAA, 19(5): 642-650 .

31.

Mittal, R. K. , Schwieger, H. and Truppat, V. (1976). A Simplified Analysis of Transverse Impact on Clamped Circular Plates. Part 1 and 2 , J. of Aero. Soc. of India, 28(1-2): 265-275 .

32.

Liew, K. M. (1996). Solving the Vibration of Thick Symmetric Laminates by Reissner Mindlin Plate Theory and the P-Titz Method , J. Sound Vib., 198(3): 343-360 .

33.

Alhassani, S. T. S. , Darvizeh, M. and Haftchenari, H. (1997). An Analytical Study of Buckling of Composite Tubes With Various Boundary Conditions , J. Composite Str., 39(1-2): 157-166 .

34.

Darvizeh, M. and Sharma, C. B. (1984). Natural Frequencies of Laminated Orthotropic Thin Circular Cylinders , Int. J. Thin Walled Str., 2(2): 207-213 .

35.

Malekzadeh, K. (1998). Static and Dynamic Analysis of Multi-layered Composite Plates for Different Boundary Conditions Using Analytical Method, MSc Thesis, Gillan University, Iran.

36.

Green, A. E. (1944). Double Fourier Series and Boundary Value Problems , In: Proc. Cambridge Philos. Soc., 40: 222-222 .

37.

Malekzadeh, K. , Khalili, M. R. and Mittal, R. K. (2004). Damped Vibration of Sandwich Plates with a Viscoelastic Soft Flexible Core: An Improved High-order Approach , In: 12th Int. Conference of Mechanical Engineering, Tarbiat Modarress Univ. Tehran, Iran, Paper Code: 120019.