Document Type : Research Paper

Authors

Department of Aerospace Engineering, MalekAshtar University of Technology, Tehran, Iran

Abstract

This article for the first time is concerned with effects of parameters as local smart stiffness and smart attached mass dimensions of dynamic behavior of thick laminated plates with attached mass. In deriving governing equations, Gark-Kant’s higher order theory is used and effects of SMA and attached mass`s stiffness taken into account and finally vibration equations of thick plate carrying attached mass contain SMA is reached by using Hamilton`s principal. Then by means of Galerkin method, mass and stiffness matrices are extracted for achieving to a standard eigenvalue vibration problem. In this problem simply supported boundary condition is used for each four edges. Some important parameters such as ratio of local stiffness to stiffness of host structure and smart attached mass dimension on main frequencies of laminated thick plate is studied. A Comparative result with those in published references is presented. These numerical results show that local stiffness due to smart attached mass has a great role on dynamic behavior of thick laminated plates that if SMA didn`t active properly or ignore the effect of attached mass`s stiffness the dynamic response of system will have a lot of changes.

Keywords

Main Subjects

[1]
Yang, P. C., Norris, C. H. and Stavsky, Y., "Elastic Wave Propagation in Heterogeneous Plates", International Journal of Solids and Structures, Vol. 2, No. 4, pp. 665-684, 1966.
[2]
Kant, T., Owen, D. R. J. and Zienkiewicz, O. C., "A Refined Higher Order Co Plate Bending Element", Computers and Structures, Vol. 15, No. 2, pp. 177–183, 1982.
[3]
Gorman, DJ. and Singal, RK., "Analytical and Experimental Study of Vibrating Rectangular Plates on Rigid Point Supports", AIAA Journal, Vol. 29, No. 5, pp. 838-844, 1991.
[4]
Rossi, R. E. and Laura, P. A. A., "Symmetric and Antisymmetric Normal Modes of a Cantilever Rectangular Plate :Effect of Poisson's Ratio and a Concentrated Mass", Journal of Sound and Vibration, Vol. 195, No. 1, pp. 142-148, 1996.
[5]
Kopmaz, O. and Telli, S., "Free Vibration of Rectangular Plate Carrying a Distributed Mass", Journal of Sound and Vibration, Vol. 251, No. 1, pp. 39-57, 2002.
[6]
Wong, W. O., "The Effect of Distributed Mass Loading on Plate Vibration Behavior", Journal of Sound and Vibration, Vol. 252, No. 3, pp. 577-583, 2002.
[7]
Alibeiglooa, A., Shakeri, M. and Kari, M. R., "Free Vibration Analysis of Antisymmetric Laminated Rectangular Plates with Distributed Patch Mass Using Third-Order Shear Deformation Theory", Ocean Engineering, Vol. 35, No. 2, pp. 183-190, 2008.
[8]
Malekzadeh, K., Tafazoli, S. and Khalili, S.M.R., "Free Vibrations of Thick Rectangular Composite Plate With Uniformly Distributed Attached Mass Including Stiffness Effect" , Journal of Composite Materials, 2010
[9]
Ostachowicz, W., krawczuk, M. and Zak, A., "Dynamic and Buckling of a Multilayer Composite Plate with Embedded SMA Wires", Composite structures, Vol. 48, No. 1-3, pp. 163-167, 2000.
[10]
Lau, K. T., Zhou, L. M. and  Tao, X. M., "Control of Natural Frequencies of a Clamped-Clamped Composite Beam with Embedded Shape Memory Alloy Wires", Composite Structures, Vol. 58, No. 1, pp. 39-47, 2002.
[11]
Mozafari, A., Malekzade, K., Ahmadi, M. and Azarnia, A. H., "Analyze Of Free Vibration Of Composite Plate With Embedded Shape Memory Alloy", in ISME16, Kerman, 2008.
[12]
Zhang, R. X., Ni, Q. Q., Masuda, A., Yamamura, T. and Iwamoto, M., "Vibration Characteristics of Laminated Composite Plates with Embedded Shape Memory Alloys", Composite Structures, Vol. 74, No. 4, pp. 389-398, 2006.
[13]
Park, J. S., Kim, J. H. and Moon, S. H., "Vibration of Thermally Post-Buckled Composite Plates Embedded with Shape Memory Alloy Fibers", Composite Structures, Vol. 63, No. 2, pp. 179–188, 2004.
[14]
Ni, Q. Q., Zhang, R. X., Natsuki, T. and Iwamoto, M., "Stiffness and Vibration Characteristics of SMA/ER3 Composites with Shap Memory Alloy Short Fibers", Composite Structures, Vol. 79, No. 4, pp. 501-–507, 2007.
[15]
Zhang, Y. and Zhao, Y. P., "A Study of Composite Beam with Shape Memory Alloy Arbitrarily Embedded Under Thermal and Mechanical Loadings", Materials and Design, Vol. 28, No. 4, pp. 1096-1115, 2007.
[16]
John, S. and Hariri, M., "Effect of Shape Memory Alloy Actuation on the Dynamic Respons of Polymeric Composite Plates", Composites Part A: Applied Science and Manufacturing, Vol. 39, No. 5, pp. 769-776, 2008.
[17]
Shokuhfar, A., Khalili, S. M. R., Ghasemi, F. A., Malekzadeh, K. and Raissi, S., "Analysis and Optimization of Smart Hybrid Composite Plates Subjected to Low-Velocity Impact Using the Response Surface Methodology (RSM) ", Thin-Walled Structures, Vol. 46, No. 11, pp. 1204-1212, 2008
[18]
Ibrahim, H. H., Yoo, H. H. and Lee, K. S ., "Aero-Termo-Mechanical Characteristics of Imperfact Shap Memory Alloy Hybrid Composite Panels", Journal o Sound and Vibration, Vol. 325, No. 3, pp. 583-596, 2009.
[19]
Kuo, S. Y.,  Shiau, L. C. and Chen, K. H., "Buckling Analysis of Shape Memory Alloy Reinforced Composite Laminates", Composite Structures, Vol. 90, No. 2, pp. 188-195, 2009.
[20]
Malekzadeha, K., Mozafari, A. and Ghasemi, F. A., "Free Vibration Response of a Multilayer Smart Hybrid Composite Plate with Embedded SMA wires", Solids And Structures, Vol. 11, No. 2, pp. 279 - 298, 2014.
[21]
Garg, A. K., Khare, R. . and Kant, T., "Higher-Order Closed-Form Solutions for Free Vibration of Laminated Composite and Sandwich Shells", Sandwich Structures and Materials, Vol. 8, No. 3, pp. 205-235, 2006.
[22]
Sadd, M. H., “Elasticity: Theory and Applications”, Second Edition, 1993.
[23]
Reddy, J. N., “Mechanics of Laminated Composite Plates and Shells”, 2nd Edition, CRC Press, 2004.
[24]
Reddy, J. N., “ Energy Principles and Variational Methods in Applied Mechanics”, 2nd Edition, John Wiley and Sons, 2002.