Free Vibration Analysis of Sandwich Plates with a Uniformly Distributed Attached Mass,Flexible Core,and Different Boundary Conditions

Abstract

The free vibration analysis of rectangular sandwich plates with a flexible core both with and without a uniformly distributed attached mass on the top facesheet is carried out using the finite element method (FEM) through ANSYS parametric design language, which is validated by several literatures through some numerical examples. The model uses the 8-node shell 99 element to model the composite laminates of the top and bottom facesheets of the sandwich plate and 20-node high-order solid 95 element in order to model the flexible PVC core. The validated finite element model is then used to study the parametric effects of geometry such as aspect ratio, length-to-thickness ratio, core thickness-to-plate thickness ratio, the size and the stiffness of the attached mass on the natural frequencies of the sandwich plate as well as the normal and shear stresses. The use of FEM also allows studying the effect of different boundary conditions for both the top and the bottom facesheets of sandwich plates with or without distributed attached mass. Numerical results that hitherto not reported in the literature have been presented in this article. The results presented in this investigation could be useful to acquire a better insight into the behavior of sandwich laminates carrying attached mass for engineering designers of sandwich structures. The results are presented and compared with the latest Numerical results found in literature.

Keywords

sandwich plate free vibration attached mass finite element method ANSYS.

Get full access to this article

View all access options for this article.

References

Chan, K.T. , Leung, T.P. and Wong, W.O. ( 1996). Free Vibration of a Simply Supported Beam Partially Loaded with a Distributed Mass, Journal of Sound and Vibration, 191: 590-597.

Chan, K.T. and Wang, X.O. ( 1997). Free Vibration of a Timoshenko Beam Partially Loaded with a Distributed Mass, Journal of Sound and Vibration, 206: 353-369.

Chan, K.T. , Wang, X.O. and Leung, T.P. ( 1998). Free Vibration of Beams with Two Sections of Distributed Mass, Journal of Vibration and Acoustics, 120: 944-948.

Rossi, R.E. and Laura, P.A.A. ( 1996). Symmetric and Anti Symmetric Normal Modes of a Cantilever Rectangular Plate: Effect of Poisson’s Ratio and a Concentrated Mass , Journal of Sound and Vibration, 195: 142-148.

Cha, P.D. (1997). Free Vibration of a Rectangular Plate Carrying a Concentrated Mass, Journal of Sound and Vibration , 207: 593-596.

Kopmaz, O. and Telli, S. ( 2002). Free Vibrations of a Rectangular Plate Carrying a Distributed Mass, Journal of Sound and Vibration, 251(1): 39-57.

Wong, W.O. ( 2002). The Effects of Distributed Mass Loading on Plate Vibration Behavior, Journal of Sound and Vibration, 252(3): 577-583.

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 Sandwich Plates with a Flexible Core: Higher Order Theory, International Journal of Solids and Structures , 35(3-4): 183-204.

10.

Frostig, Y. and Thomsen, O.T. (2004). Higher Order Free Vibration of Sandwich Plates with a Flexible Core, International Journal of Solids and Structures, 41: 1697-1724.

11.

Mijia, Y. and Pizhong, Q. ( 2005). Higher Order Theory Impact Modeling of Sandwich Structures with a Flexible Core, International Journal of Solids and Structures, 42(10): 5460-5490.

12.

Malekzadeh, K. , Khalili, M.R. and Mittal, R.K. (2005). Local and Global Damped Vibrations of Plates with a Viscoelastic Soft Flexible Core: An Improved High-order Approach, Journal of Sandwich Structures and Materials, 7(5): 431-456.

13.

Malekzadeh, K. , Khalili, M.R. , Olsson, R. and Jafari, A. (2006). Higher Order Dynamic Response of Composite Sandwich Plates with a Flexible Core Under Simultaneous Low-velocity Impacts of Multiple Small Masses, International Journal of Solids and Structures, 43: 6667-6687.

14.

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

15.

Nayak, A.K. , Moy, S.S.J. and Shenoi, R.A. (2002). Free Vibration Analysis of Composite Sandwich Plates Based on Reddy’s Higher-order Theory, Composites (Part B 33), 33(7): 505-519.

16.

Mathews, F.L. , Davies, G.A.O. , Hitchings, D. and Soutis, C. (2000). Finite Element Modeling of Composite Materials and Structures, CRC Press, Boca Raton, FL.

17.

Ochoa, O.O. and Reddy, J.N. ( 1992). Finite Element Analysis of Composite Laminates, Kluwer Academic Publishers, Dordrecht.

18.

Khatua, T.P. and Cheung, Y.K. (1972). Triangular Element for Multi-layer Sandwich Plates, Journal of Engineering Mechanics, ASCE, 98: 1225-1238.

19.

Sheikh, A.H. , Halder, S. and Sengupta, D. ( 2002). Vibration of Plates in Different Situations Using a High Precision Shear Deformable Element, Journal of Sound and Vibration , 253: 329-345.

20.

Sheikh, A.H. , Halder, S. and Sengupta, D. ( 2004). Free Flexural Vibration of Composite Plates in Different Situations Using a High Precision Triangular Element, Journal of Vibration and Control, 10: 371-386.

21.

ANSYS Software Release 10, Theory Reference (http://www.ansys.com).

22.

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

23.

Bathe, K.-J. ( 1996). Finite Element Procedures, Prentice Hall Inc, Englewood Cliffs, NJ.

24.

Wang, T. , Sokolinsky, V. , Rajaram, S. and Nutt, S.R. ( 2008). Consistent Higher-order Free Vibration Analysis of Composite Sandwich Plates, Composite Structures, 82(4): 609-621.