Document Type: Research Paper


1 University of Tabriz

2 Tabriz of University


The purpose of this paper is control of simply supported flexible core sandwich beam's linear vibration equipped with piezoelectric patches under different loads. The effects of external forces imposed on sandwich beam can be reached to a minimum value by designing an appropriate controller and control the beam's vibration. Three-layer sandwich beam theory is used for analytical modeling of sandwich beam vibration. Euler-Bernoulli beam theory and linear displacement field are used for the face-sheets and the soft core, respectively. The piezoelectric stress resultants are expressed in terms of Heaviside discontinuity functions. Governing equations of motion are obtained using Hamilton’s principle. The state space equations of system are derived from governing equations of motion, by defining suitable state variables and using Galerkin’s method. The controller is designed using linear quadratic Gaussian (LQG) technique and Kalman filter is used to estimate the state of the system. The numerical results are compared with those available in the literature. The obtained results show that the controller can play a big role toward damping out the vibration of the sandwich beam. It also shows the difference between the vibration of top face sheets and bottom face sheets because of the flexibility of the core and the situations of sensor and actuator on the top or bottom face sheets have an important role on the dynamic response of sandwich beam.

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[1] L. Librescu, and T. Hause, “Recent developments in the modeling and behavior of advanced sandwich constructions: a survey,” Composite Structures, Vol. 48, pp. 1-17, (2000).

[2] H. Biglari,and A. Jafari, “Static and free vibration analyses of doubly curved composite sandwich panels with soft core based on a new three-layered mixed theory,” Composite Structures, Vol. 92, pp. 2684- 2694, (2010).

[3] M. Ganapathi, B.P. Patel, and D.P. Makhecha, “Nonlinear dynamic analysis of thick composite/sandwich laminates using an accurate higher-order theory,” Composites Part B: Engineering, Vol. 35, No. 4, pp. 345-355, (2004).

[4] J. L. Mantari, and C. Guedes Soares, “Generalized layerwise HSDT and finite element formulation for symmetric laminated and sandwich composite plates,” Composite Structures, Vol. 105, pp. 319- 331, (2013).

[5] H. Abramovich, and B. Pletner, “Actuation and sensing of piezolaminated sandwich type structures,” Composite Structure, Vol. 38, No.1–4, 17-27, (1997).

[6] W. C. H. C. Chang, and S. S. Gai, “Forced vibration of composite sandwich beams with piezoelectric sensors and actuators,” 4th Pacific International Conference on Aerospace Science and Technology, Kaohsiung, Taiwan, 21-23, (2001).

[7] S. Kapuria, A. Ahmed, and P. C. Dumir, ”An efficient coupled zigzag theory for dynamic analysis of piezoelectric composite and sandwich beams with damping,” Journal of Sound and Vibration, Vol. 279, No. 1–2, pp. 345- 371, (2005).

[8] L. Azrar, S. Belouettar, and J. Wauer, “Nonlinear vibration analysis of actively loaded sandwich piezoelectric beams with geometric imperfection,” Computers and structures, Vol. 86, No. 2, pp. 2191-182, (2008).

[9] K. Ramesh Kumar, and S. Narayanan, “Active vibration control of beams with optimal placement of piezoelectric sensor/actuator pairs,” Smart Materials and Structures, Vol. 17, No. 5, pp. 1-15, (2008).

[10] P. Dash, and B. N. Singh, “Nonlinear free vibration of piezoelectric laminated composite plate,” Finite Elements in Analysis and Design, Vol. 45, No. 10, pp. 686-694, (2009).

[11] M. Azadi, E. Azadi, and M. Roopaei, “Adaptive inverse dynamics control for vibration suppression,” World Applied Sciences Journal, Vol. 12, No. 12, pp. 2343-2351, (2011).

[12] D. Chhabra, P. Chandna, and G. Bhushan, “Design and analysis of smart structures for active vibration control using piezocrystals,” International Journal of Engineering and Technology, Vol. 1, No. 3, pp. 153-162 , (2011).

[13] A. Moutsopoulou, G. Stavroulakis, and T. Pouliezos. “Simulation and modelling of smart beams with robust control subjected to wind induced vibration," Open Journal of Civil Engineering, Vol. 2, No. 3, pp. 106-114, (2011).

[14] E. Hamed, and O. Rabinovitch, “Modeling and dynamics of sandwich beams with a viscoelastic soft core,” AIAA Journal, Vol. 47, No. 9, pp. 2194-2211, (2009).

[15] J. N. Reddy, “On laminated composite plates with integrated sensors and actuators,” Engineering Structures, Vol. 21, No. 7, pp. 568-593, (1999).

[16] E. Padoin, O. Menuzzi, E. A. Perondi, and J. Ono Fonseca, ”Modeling and LQR/LQG control of a cantilever beam using piezoelectric material”, 22nd International congress of mechanical engineering-COBEM 2013, Ribeirão Preto, SP, Brazil. November 3-7, (2013).

[17] Y. M. Huang, and T. J. Chen,” Passive piezoelectric absorbers on supperessing vibration of a rotating beam”, Twelfth International Congress on Sound and Vibration, (2005).

[18] B. D. O. Anderson, and J. B. Moore, "Optimal Control, Linear Quadratic Methods," Prentice-Hall Inc., New Jersey, (1989).

[19] A. R. Damanpack, M. Bodaghi, M. M. Aghdam, and M. Shakeri, ”Active control of geometrically non-linear transient response of sandwich beams with a flexible core using piezoelectric patches", Composite Structures, Vol. 100, pp. 517– 531, (2013).