Abstract
This paper presents an analysis of the active control of random vibration for laminated composite plates using piezoelectric fiber reinforced composites (PFRC). With Hamilton’s principle and the Rayleigh-Ritz method, the equation of motion for the resulting electromechanical coupling system is derived. A velocity feedback control rule is employed to obtain an effective active damping in the suppression of random vibration. The power spectral density and mean-square displacements of the random vibration for laminated plates under different control gains are simulated and the validity of the present control strategy is confirmed. The effect of piezoelectric fiber orientation in the PFRC layer on the random vibration suppression is also investigated. The analytical methodology can be expanded to other kinds of random vibration.
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References
Lee, C.K., Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part I, governing equations and reciprocal relationships. Journal of Acoustical Society of America, 1990, 87: 1144–1158.
Lammering, R., The application of a finite shell element for composite containing piezoelectric polymers in vibration control. Computers and Structures, 1991, 41: 1101–1109.
Sonti, V.R. and Jones, J.D., Curved piezoactuator model for active vibration control of cylindrical shells. American Institute of Aeronautics and Astronautics Journal, 1996, 34(5): 1034–1040.
Lin, J.C. and Nien, M.H., Adaptive control of a composite cantilever beam with piezoelectric damping-modal actuators/sensors. Composite Structures, 2005, 70: 170–176.
Hagood, N.W., Chung, W.H. and von Flotow, A., Modelling of piezoeletric actuator dynamics for active structural control. Journal of Intelligent Material Systems and Structures, 1990, 1: 327–354.
Pietrzakowski, M., Piezoelectric control of composite plate vibration, Effect of electric potential distribution. Computers and Structures, 2008, 86: 948–954.
Li, F.M., Kishimoto, K., Wang, Y.S. Chen, Z.B. and Huang, W.H., Vibration control of beams with active constrained layer damping. Smart Materials and Structures, 2008, 17: 065036.
Li, F.M., Song, Z.G. and Chen, Z.B., Active vibration control of conical shells using piezoelectric materials. Journal of Vibration and Control, 2012, 18: 2234–2256.
Li, F.M., Active aeroelastic flutter suppression of a supersonic plate with piezoelectric material. International Journal of Engineering Science, 2012, 51: 190–203.
Li, F.M., Kishimoto, K. and Huang, W.H., The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh-Ritz method. Mechanics Research Communications, 2009, 36: 595–602.
Witt, M. and Sobczyk, K., Dynamic response of laminated plates to random loading. International Journal of Solids and Structures, 1980, 16: 231–238.
Mei, C. and Prasad, C.B., Effects of large deflection and transverse shear on response of rectangular symmetric composite laminates subjected to acoustic excitation. In: AIAA Dynamics Specialists Conference, Monterey, CA, 1987: 809–826.
Cederbaum, G. Librescu, L. and Elishakoff, I., Random vibrations of laminated plates modeled within the first order shear deformation theory. Composite Structures, 1989, 12: 97–111.
Van den Nieuwenhof, B.V. and Coyette, J.P., Modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties. Computer Methods in Applied Mechanics and Engineering, 2003, 192: 37053729.
Gao, W. Zhang, N. and Ji, J.C., A new method for random vibration analysis of stochastic truss structures. Finite Elements in Analysis and Design, 2009, 45: 190199.
Zhao, L. and Chen, Q., Neumann dynamic stochastic finite element method of vibration for structures with stochastic parameters to random excitation. Computers & Structures, 2000, 77: 651657.
Li, J. and Liao, S.T., Dynamic response of linear stochastic structures under random excitation. Acta Mechanica Sinica, 2002, 34: 416424.
Narita, Y., Combinations for the free-vibration behaviors of anisotropic rectangular plates under general edge conditions. ASME Journal of Applied Mechanics, 2000, 67: 568–573.
Narita, Y., Layerwise optimization for the maximum fundamental frequency of laminated composite plates. Journal of Sound and Vibration, 2003, 263: 1005–1016.
Ray, M.C. and Mallik, N., Active control of laminated composite beams using a piezoelectric fiber reinforced composite layer. Smart Materials and Structures, 2004, 13: 146–152.
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Project supported by the National Natural Science Foundation of China (Nos. 11502159 and 11390362), Natural Science Foundation of Shanxi (No. 2015021014), the Top Young Academic Leaders of High Learning Institutions of Shanxi, Shanxi Scholarship Council of China, the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.
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Li, J., Ma, Z., Wang, Z. et al. Random vibration control of laminated composite plates with piezoelectric fiber reinforced composites. Acta Mech. Solida Sin. 29, 316–327 (2016). https://doi.org/10.1016/S0894-9166(16)30164-1
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DOI: https://doi.org/10.1016/S0894-9166(16)30164-1