Control of Nonlinear Vibration in Bi-Stable Composite Plates using Fuzzy Logic
Authors
Abstract
Having two stable configurations and no need to any permanent energy sources for remaining in each of these stable states, bi-stable composite plates have gained many applications. This paper has concentrated on control and dynamic response of cross ply bi-stable composite plates (0.90). To do this, using Hamilton principle , Rayleigh-Ritz method, and a MATLAB programme specifically designed for this study, have been applied in order to extract the governing equation of motions in plates. Then, in order to control the large vibration of the cross ply bi-stable plate, a fuzzy controller was proposed using a fuzzy logic and its prformance was simulated by Simulink in Matlab environment. In order to simulate the real conditions on the controller performance, the effect of disturbances and time delay on the responses of controller were also investigated.
Keywords
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11. Vogl, G. A., and Hyer, M. W., “Natural Vibration of Unsymmetric Cross-Ply Laminates”, Journal of Sound & Vibration, Vol. 330, pp. 4764-4779, 2011.
12. Fuhong, D., Hao, L., and Shanyi, D., “A Multi-stable Wavy Skin Based on Bi-Stable Laminates” Composites: Part A, Vol. 45, pp. 102-108, 2013.
13. Fuhong, D., Hao, L., and Shanyi, D., “A Multi-Stable Lattice Structure and Its Snap-through Behavior Among Multiple States”, Composite Structures, Vol. 97, pp. 56-63, 2013.
14. Arrieta, A. F., Bilgen, O., Friswell, M. I., and Ermanni, P., “Modelling and Configuration Control of Wing-Shaped Bi-Stable Piezoelectric Composites under Aerodynamic Loads”, Aerospace Science and Technology, Vol. 29, pp. 453-461, 2013.
15. Kyriazoglou, C. and Guild, F. J., “Finite Element Prediction of Damping of Composite GFRP and CFRP Laminates - a Hybrid Formulation - Vibration Damping Experiments and Rayleigh Damping”, Composites Science and Technology, Vol. 66, pp. 487-498, 2006.
2. Hyer, M. W., “Calculations of the Room-Temperature Shapes of Unsymmetric Laminates”, Journal of Composite Materials, Vol. 15, pp. 296-310, 1981.
3. Hyer, M. W., “The Room-Temperature Shapes of Four-Layer Asymmetric Cross-Ply Laminates”, Journal of Composite Materials, Vol. 16, pp. 318-340, 1982.
4. Moore, M., Ziaei-Rad, S., and Salehi, H., “Thermal Response and Stability Characteristics of Bi-Stable Composite Laminates by Considering Temperature Dependent Material Properties and Resin Layers”, Applied Composite Materials, Vol. 20, No. 1, pp. 87-106, 2013.
5. Moore, M., Ziaei-Rad, S., and Firouzian-Nejad, A., “Temperature-Curvature Relationships in Asymmetric Angle Ply Laminates by Considering the Effects of Resin Layers and Temperature Dependency of Material Properties”, Journal of Composite Materials, Vol. 48, No. 9, pp. 1071-1089, 2014.
6. Mattioni, F., Weaver, P. M., and Friswell, M. I., “Multistable Composite Plates with Piecewise Variation of Lay-up in the Planform”, International Journal of Solids and Structures, Vol. 46, pp. 151-164, 2009.
7. Dano, M. L., and Hyer, M. W., “SMA-Induced Snap-through of Unsymmetric Fiber-Reinforced Composite Laminates”, Journal of Solids and Structures, Vol. 40, pp. 5949-5972, 2003.
8. Portela, P. M., Camanho, P. P., Weaver, P. M., and Bond, I. P., “Analysis of Morphing Multistable Structures Actuated by Piezoelectric Patches”, Composite Structures, Vol. 86, pp. 347-356, 2008.
9. Schultz, M. R., Hyer, M. W., Williams, R. B., Wilkie, W. K., and Inman, D. J, “Snap through of Unsymmetric Laminates Using Piezocomposite Actuators”, Composites Science and Technology, Vol. 66, pp. 2442-2448, 2006.
10. Diaconu, C. G., Weaver, P. M., and Arrieta, A. F., “Dynamic Analysis of Bi-Stable Composite Plate”, Journal of Sound & Vibration, Vol. 322, pp. 987-1004, 2009.
11. Vogl, G. A., and Hyer, M. W., “Natural Vibration of Unsymmetric Cross-Ply Laminates”, Journal of Sound & Vibration, Vol. 330, pp. 4764-4779, 2011.
12. Fuhong, D., Hao, L., and Shanyi, D., “A Multi-stable Wavy Skin Based on Bi-Stable Laminates” Composites: Part A, Vol. 45, pp. 102-108, 2013.
13. Fuhong, D., Hao, L., and Shanyi, D., “A Multi-Stable Lattice Structure and Its Snap-through Behavior Among Multiple States”, Composite Structures, Vol. 97, pp. 56-63, 2013.
14. Arrieta, A. F., Bilgen, O., Friswell, M. I., and Ermanni, P., “Modelling and Configuration Control of Wing-Shaped Bi-Stable Piezoelectric Composites under Aerodynamic Loads”, Aerospace Science and Technology, Vol. 29, pp. 453-461, 2013.
15. Kyriazoglou, C. and Guild, F. J., “Finite Element Prediction of Damping of Composite GFRP and CFRP Laminates - a Hybrid Formulation - Vibration Damping Experiments and Rayleigh Damping”, Composites Science and Technology, Vol. 66, pp. 487-498, 2006.
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