A. E. Alshorbagy, M. A. Eltaher, and M. Ff, Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, vol.35, pp.412-425, 2011.

M. Aminbgahai, J. Murin, and V. Hutis, Modal analysis of the FGM-beams with continuous transversal symmetric and longitudinal variation of material properties with effect of large axial force, Engineering Structures, vol.34, pp.314-329, 2012.

K. K. Ang and W. Sy, Weighted energy linear quadratic regulator vibration control of piezoelectric composite plates, Smart Materials and Structures, vol.11, pp.98-106, 2002.

H. A. Atmane, A. Tounsi, S. A. Meftah, and H. A. Belhadj, Free vibration behavior of exponential functionally graded beams with varying cross-section, Journal of Vibration and Control, vol.17, pp.311-318, 2010.

M. Aydogdu and V. Taskin, Free vibration of functionally graded beams with simply supported edges, Materials and Design, vol.28, pp.1651-1656, 2006.

V. Balamurugan and S. Narayanan, Shell finite element for smart piezoelectric composite plate/shell structures and its application to the study of active vibration control, Finite Elements in Analysis and Design, vol.37, pp.713-738, 2001.

A. Benjeddou, Advances in piezoelectric finite element modeling of adaptive structural elements: A survey, Computers and Structures, vol.76, pp.347-363, 2000.

I. Bruant, G. Coffignal, . Le´ne´fle´ne´le´ne´f, and . Verge´mverge´m, Active control of beam structures with piezoelectric actuators and sensors: Modeling and simulation, Smart Materials and Structures, vol.10, pp.404-408, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01978408

I. Bruant, P. F. Polit, and O. , Active control of laminated plates using a piezoelectric finite element. Mechanics of, Advanced Materials and Structures, vol.15, pp.276-290, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01366936

I. Bruant, L. Gallimard, and S. Nikoukar, Optimal piezoelectric actuator and sensor location for active vibration control, using genetic algorithm, Journal of Sound and Vibration, vol.329, pp.1615-1635, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01689879

B. Chomette, R. D. Chesne´schesne´s, and L. Gaudiller, Semi adaptive modal control of on-board electronic boards using an identification method, Smart Materials and Structures, vol.17, p.65019, 2008.

A. Doroushi, M. R. Eslami, and A. Komeili, Vibration analysis and transient response of an FGPM beam under thermo-electro-mechanical loads using higher-order shear deformation theory, Journal of Intelligent Material Systems and Structures, vol.22, pp.231-243, 2011.

V. Fakhari and A. Ohadi, Nonlinear vibration control of functionally graded plate with piezoelectric layers in thermal environment, Journal of Vibration and Control, vol.17, pp.448-469, 2010.

Y. Fu, W. J. Mao, and Y. , Nonlinear vibration and active control of functionally graded beams with piezoelectric sensors and actuators, Journal of Intelligent Material Systems and Structures, vol.22, pp.2093-2102, 2013.

L. Gaudiller and J. Der-hagopian, Active control of flexible structures using a minimum number of components, Journal of Sound and Vibration, vol.193, pp.713-741, 1996.

A. Gharib, M. Salehi, and S. Fazeli, Deflection control of functionally graded material beams with bonded piezoelectric sensors and actuators, Materials Science and Engineering A, vol.498, pp.110-114, 2008.

G. Giunta, D. Crisafulli, S. Belouettar, and E. Carrera, Hierarchical theories for the free vibration analysis of functionally graded beams, Composite Structures, vol.94, pp.68-74, 2011.

A. Hac and L. Liu, Sensor and actuator location in motion control of flexible structures, Journal of Sound and Vibration, vol.167, pp.239-261, 1993.

X. Q. He, T. Y. Ng, S. Sivashanker, and K. M. Liew, Active control of FGM plates with integrated piezoelectric sensors and actuators, International Journal of Solids and Structures, vol.38, pp.1641-1655, 2001.

A. K. Jha and D. J. Inman, Optimal sizes and placements of piezoelectric actuators and sensors for an inflated torus, Journal of Intelligent Material Systems and Structures, vol.14, pp.563-576, 2003.

D. K. Jha, T. Kant, and R. K. Singh, A critical review of recent research on functionally graded plates, Composite Structures, vol.96, pp.833-849, 2013.

T. Kailath, Linear Systems, 1980.

S. Kapuria, M. Bhattacharyya, and A. N. Kumar, Bending and free vibration response of layered functionally graded beams: A theoretical model and its experimental validation, Composite Structures, vol.82, pp.390-402, 2007.
DOI : 10.1016/j.compstruct.2007.01.019

M. H. Kargarnovin, M. M. Najafizadeh, and N. S. Viliani, Vibration control of functionally graded material plate patched with piezoelectric actuators and sensors under a constant electric charge, Smart Materials and Structures, vol.16, pp.1252-1259, 2007.

S. Kondoh, Y. , C. Inoue, and K. , The positioning of sensors and actuators in the vibration control of flexible systems, JSME International Journal, vol.33, pp.145-152, 1990.

Z. K. Kusculuoglu and T. J. Royston, Finite element formulation for composite plates with piezoceramic layers for optimal vibration control applications, Smart Materials and Structures, vol.14, pp.1139-1153, 2005.
DOI : 10.1088/0964-1726/14/6/007

X. F. Li, A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams, Journal of Sound and Vibration, vol.318, pp.1210-1229, 2008.
DOI : 10.1016/j.jsv.2008.04.056

K. M. Liew, S. Sivashanker, X. Q. He, and T. Y. Ng, The modeling and design of smart structures using functionally graded materials and piezoelectrical sensor/actuator patches, Smart Materials and Structures, vol.12, pp.647-655, 2003.
DOI : 10.1088/0964-1726/12/4/316

R. Mirzaeifar, H. Bahai, and S. Shahab, Active control of natural frequencies of FGM plates by piezoelectric sensor/ actuator pairs, Smart Materials and Structures, vol.17, p.45003, 2008.
DOI : 10.1088/0964-1726/17/4/045003

S. Narayanan and V. Balamurugan, Finite element modelling of piezolaminated smart structures for active vibration control with distributed sensors and actuators, Journal of Sound and Vibration, vol.262, pp.529-562, 2003.
DOI : 10.1016/s0022-460x(03)00110-x

S. Narayanan and V. Balamurugan, Functionally graded shells with distributed piezoelectric sensors and actuators for active vibration control. IUTAM symposium on multi functional material structures and systems, pp.3-13, 2008.
DOI : 10.1007/978-90-481-3771-8_1

T. Nestorovic and M. Trajkov, Active control of smart structures-An overall approach, Facta Universitatis: Architecture and Civil Engineering, vol.8, pp.35-44, 2010.
DOI : 10.2298/fuace1001035n

O. Polit and M. Touratier, High-order triangular sandwich plate finite element for linear and non-linear analyses, Computer Methods in Applied Mechanics and Engineering, vol.185, pp.305-324, 2000.
DOI : 10.1016/s0045-7825(99)00264-9
URL : https://hal.archives-ouvertes.fr/hal-01366943

A. Preumont, Vibration Control of Active Structures: An Introduction, 1999.

J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2004.
DOI : 10.1201/b12409

G. G. Sheng and X. Wang, Active control of functionally graded laminated cylindrical shells, Composite Structures, vol.90, pp.448-457, 2009.
DOI : 10.1016/j.compstruct.2009.04.017

M. Simsek, Fudamental frequency analysis of functionally graded beams by using different higher-order beam theories, Nuclear Engineering and Design, vol.240, pp.697-705, 2010.

M. Simsek and T. Kocaturk, Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load, Composite Structures, vol.90, pp.465-473, 2009.

S. A. Sina, H. M. Navazi, and H. Haddadpour, An analytical method for free vibration analysis of functionally graded beams, Materials and Design, vol.30, pp.741-747, 2009.
DOI : 10.1016/j.matdes.2008.05.015

H. J. Xiang and J. Yang, Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction, Composites: Part B, vol.39, pp.292-303, 2008.

R. X. Yao and Z. F. Shi, Steady-state forced vibration of functionally graded piezoelectric beams, Journal of Intelligent Material Systems and Structures, vol.22, pp.769-779, 2011.

M. Yiqi and F. Yiming, Nonlinear dynamic response and active vibration control for piezoelectric functionally graded plate, Journal of Sound and Vibration, vol.329, pp.2015-2028, 2010.

S. J. Zheng, F. Dai, and Z. Song, Active control of piezothermoelastic FGM shells using integrated piezoelectric sensor/actuator layers, International Journal of Applied Electromagnetics and Mechanics, vol.30, pp.107-124, 2009.