The paper is focused on the application of artificial neural networks (ANN) in predicting the natural frequency of laminated composite plates under clamped boundary condition. For training and testing of the ANN model, a number of finite element analyses have been carried out using D-optimal design in the design of experiments (DOE) by varying the fibre orientations, –45?, 0?, 45? and 90?. The composite plate is modeled using linear layered structural shell element. The natural frequencies were found by analyses which were done by finite element (FE) analysis software. The ANN model has been developed using multilayer perceptron (MLP) back propagation algorithm. The adequacy of the developed model is verified by coefficient of determination (R). It was found that the R2 (R: coefficient of determination) values are 1 and 0.998 for train and test data respectively. The results showed that, the training algorithm of back propagation was sufficient enough in predicting the natural frequency of laminated composite plates. To judge the ability and efficiency of the developed ANN model, absolute relative error has been used. The results predicted by ANN are in very good agreement with the finite element (FE) results. Consequently, the D-optimal design and ANN are shown to be effective in predicting the natural frequency of laminated composite plates.
KeywordsDOELaminated Composite PlatesANNMLPD-Optimal DesignFinite Element Analysis
A. Todoroki and T. Ishikawa, “Design of Experiments for Stacking Sequence Optimizations with Genetic Algorithm Using Response Surface Approximation,” International Journal of Composite Structures, Vol. 64, No. 3-4, 2004, pp. 349-357. doi:10.1016/j.compstruct.2003.09.004
K. M. Dutt and H. K. Shivanand, “An Experimental Approach to Free Vibration Response of Carbon Composite Laminates,” International Journal of Advanced Engineering & Application, No. 66, 2011, pp. e66-e68.
B. R. Reddy, K. Ramji and B. Satyanarayana, “Free Vibration Analysis of Carbon Nanotube Reinforced Laminated Composite Panels,” World Academy of Science, Engineering and Technology, Vol. 80, 2011, pp. 768-772.
H.-Y. Lin, J.-H. Huang and C.-C. Ma, “Vibration Analysis of Angle-Ply Laminated Composite Plates with an Embedded Piezoceramic Layer,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 50, No. 9, 2003, pp. 1084-1099. doi:10.1109/TUFFC.2003.1235320
T. Kant and J. R. Kommineni, “Large Amplitude Free Vibration Analysis of Cross-ply Composite and Sandwich Laminates with a Refined Theory and Co Finite Elements,” Computers and Structures, Vol. 50, No. 1, 1994, pp. 123-134. doi:10.1016/0045-7949(94)90443-X
S. Latheswary, K. V. Valsarajan, et al., “Free Vibration Analysis of Laminated Plates Using Higher-Order Shear Deformation Theory,” IE(I) Journal-AS, Vol. 85, 2004, pp. 18-24.
M. Prabhakaran and C. Sivakandhan, “Analysis of Mechanical Properties and Free Vibration Response of Composite Laminates,” International Journal of Mechanical & Industrial Engineering, Vol. 1, No. 1, 2011, pp. 84-88.
T. Kant and K. Swaminathan “Analytical Solutions for Free Vibration of Composite and Sandwich Plates Based on Higher-Order Refined Theory,” Composite Structures, Vol. 53, No. 1, 2001, pp. 73-85. doi:10.1016/S0263-8223(00)00180-X
I. Kü?ükrendeci1 and ?. K. Morgül, “The Effects of Elastic Boundary Conditions on the Linear Free Vibrations,” Scientific Research and Essays, Vol. 6, No. 19, 2011, pp. 3949-3958.
X. Zhao, K. M. Liew and T. Y. Ng, “Vibration Analysis of Laminated Composite Cylindrical Panels via a Mesh- free Approach,” International Journal of Solids and Structures, Vol. 40, No. 1, 2003, pp. 161-180. doi:10.1016/S0020-7683(02)00475-4
M. Aydo?gdu and T. Timarci, “Free Vibrations of Anti-symmetric Angle-Ply Laminated Thin Square Composite Plates,” Turkish Journal of Engineering and Environmental Science, Vol. 31, No. 4, 2007, pp. 243-249.
G. R. Liu, X. Zhao, K. Y. Dai, Z. H. Zhong, G. Y. Li and X. Han, “Static and Free Vibration Analysis of Laminated Composite Plates Using the Conforming Radial Point Interpolation Method,” Composites Science and Technology, Vol. 68, No. 2, 2008, pp. 354-366. doi:10.1016/j.compscitech.2007.07.014
R. K. Khare, T. Kant and A. K. Garg, “Free Vibration of Composite and Sandwich Laminates with a Higher-Order Facet Shell Element,” Journal of Composite Structures, Vol. 65, No. 3-4, 2004, pp. 405-418. doi:10.1016/j.compstruct.2003.12.003
M. K. Rao and Y. M. Desai, “Analytical Solutions for Vibrations of Laminated and Sandwich Plates Using Mixed Theory,” Composite Structures, Vol. 63, No. 3-4, 2004, pp. 361-373. doi:10.1016/S0263-8223(03)00185-5
B. P. Patel, M. Ganapathi and S. Kamat, “Free Vibration Characteristics of Laminated Composite Joined Conical- Cylindrical Shells,” Journal of Sound and Vibration, Vol. 237, No. 5, 2000, pp. 920-930. doi:10.1006/jsvi.2000.3018
C. A. Shankara and N. G. R. Iyengar, “AC0 Element for the Free Vibration Analysis of Laminated Composite Plates,” Journal of Sound and Vibration, Vol. 191, No. 5, 1996, pp. 721-738. doi:10.1006/jsvi.1996.0152
P. Afshari, “Free Vibration Analysis of Composite Plates,” Journal of Pressure Vessel Technology, Vol. 122, No. 3, 2000, pp. 390-399. doi:10.1115/1.556198
M. H. Sadr, H. G. Bargh, M. K. Nejadi and H. Pourzand, “Free Vibration Analysis of Rotating Laminated Composite Panels Using Finite Strip Method with Modified Shape Functions,” Proceedings of the ASME 2011 International Mechanical Engineering Congress & Exposition, Denver, 11-17 November 2011, pp. 1-7.
T. Kant and Mallikarjuna, “A Higher-Order Theory for Free Vibration of Asymmetrically Laminated Composite and Sandwich Plate-Finite Element Evaluations,” Computers and Structure, Vol. 32, No. 5, 1989, pp. 1125- 1132.
A. R. Reddy, B. S. Reddy and K. V. K. Reddy, “Application of Design of Experiments and Artificial Neural Networks for Stacking Sequence Optimizations of Laminated Composite Plates,” International Journal of Engineering, Science and Technology, Vol. 3, No. 6, 2011, pp. 295- 310.
ANSYS, “Theory Manual,” 2010.
R. H. Meyers and D. C. Montgomery, “Response Surface Methodology: Process and Product Optimization Using Designed Experiments,” John Wiley & Sons, New York, 1995.
J. Principe, C. Lefebvre, G. Lynn, C. Fancourt and D. Wooten, “Neurosolutions Documentation.” http://www.neurosolutions.com/downloads/documentation.html
R. Vaziri, X. Quan and M. D. Olson, “Impact Analysis of Laminated Composite Plates and Shells by Super Finite Element,” International Journal of Impact Engineering, Vol. 18, No. 7-8, 1996, pp. 765-782. doi:10.1016/S0734-743X(96)00030-9
J. M. Whitney, “Structural Analysis of laminated Anisotropic Plates,” Technomic Publishing Co., Inc., Lancaster, 1987.
M. T. Ahamadian and M. S. Zangeneh, “Forced Vibration Analysis of Laminated Rectangular Plates Using Super Elements,” Journal of Scientia Iranica, Vol. 10, No. 2, 2003, pp. 260-265.
R. Rikards, A. Chate and O. Ozolinsh, “Analysis for Buckling and Vibrations of Composite Stiffened Shells and Plates,” Composite Structures, Vol. 51, No. 4, 2001, pp. 361-370. doi:10.1016/S0263-8223(00)00151-3
D. C. Montgomery, “Design and Analysis of Experiments,” 5th Edition, Wiley, New York, 2001.