Free vibration characteristics of a functionally graded beam by finite element method, Appl. Math. Model, vol.35, pp.412-425, 2011. ,
Modal analysis of the FGM-beams with continuous transversal symmetric and longitudinal variation of material properties with effect of large axial force, Eng. Struct, vol.34, pp.314-329, 2012. ,
Controllability measures and actuator placement in oscillatory systems, Int. J. Control, vol.33, issue.3, pp.565-574, 1981. ,
Shell finite element for smart piezoelectric composite plate/shell structures and its application to the study of active vibration control, Finite Elem. Anal. Des, vol.37, pp.713-738, 2001. ,
Optimal locations and orientations of piezoelectric transducers on cylindrical shell based on gramians of contributed and undesired Rayleigh-Ritz modes using genetic algorithm, J. Sound Vib, vol.333, pp.1224-1244, 2014. ,
Optimal location of piezoelectric actuators on a beam, Proceedings of Active 97, pp.635-649, 1997. ,
Active control of beam structures with piezoelectric actuators and sensors: modeling and simulation, Smart Mater. Struct, vol.10, pp.404-408, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-01978408
Optimal location of actuators and sensors in active vibration control, J. Intell. Mater. Syst. Struct, vol.16, pp.197-206, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-01978500
Improved active control of a functionally graded material beam with piezoelectric patches, J. Vib. Control, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01421512
Exact closed-form solution for the vibration modes of the Euler-Bernoulli beam with multiple open cracks, J. Sound Vib, vol.327, pp.473-489, 2009. ,
The exact explicit dynamic stiffness matrix of multi-cracked Euler-Bernoulli beam and applications to damaged frame structures, J. Sound Vib, vol.332, pp.3049-3063, 2013. ,
Piezoelectric actuator design for vibration suppression: placement and sizing, J. Guid. Control Dyn, vol.16, issue.5, pp.859-864, 1993. ,
Multiobjective design of actively controlled structures using a hybrid optimizatoon method, Int. J. Numer. Methods Eng, vol.38, pp.3383-3401, 1995. ,
Piezo actuator placement and sizing for good control effectiveness and minimal change in original system dynamics, Smart Mater. Struct, vol.15, pp.1661-1672, 2006. ,
Nonlinear vibration control of functionally graded plate with piezoelectric layers in thermal environment, J. Vib. Control, vol.17, pp.448-469, 2010. ,
Recent advances in optimization of smart structures and actuators, J. Intell. Mater. Syst. Struct, vol.14, pp.207-215, 2003. ,
Nonlinear vibration and active control of functionally graded beams with piezoelectric sensors and actuators, J. Intell. Mater. Syst. Struct, vol.22, pp.2093-2102, 2013. ,
Simultaneous placement of actuators and sensors, J. Sound Vib, vol.228, issue.4, pp.915-922, 1999. ,
Deflection control of functionally graded material beams with bonded piezoelectric sensors and actuators, Mater. Sci. Eng. A, vol.498, pp.110-114, 2008. ,
Hierarchical theories for free vibration analysis of functionally graded beams, Compos. Struct, vol.94, pp.68-74, 2011. ,
Optimal actuator and sensor placement in flexible structures using closed-loop criteria, J. Sound Vib, vol.312, pp.210-233, 2007. ,
Sensor and actuator location in motion control of flexible structures, J. Sound Vib, vol.167, pp.239-261, 1993. ,
An optimization approach to optimal placement of collocated piezoelectric actuators and sensors on a thin plate, Mechatronics, vol.13, pp.27-47, 2003. ,
Active control of FGM plates with integrated piezoelectric sensors and actuators, Int. J. Solids Struct, vol.38, pp.1641-1655, 2001. ,
A new approach for free vibration of axially functionally graded beams with non-uniform cross-section, J. Sound Vib, vol.329, pp.2291-2303, 2010. ,
Free vibration of axially functionally graded Timoshenko beams with non-uniform cross-section, Compos. Part B, vol.45, pp.1493-1498, 2013. ,
Optimal sensor/actuator placement for active vibration control using explicit solution of algebraic Riccati equation, J. Sound Vib, vol.229, issue.5, pp.1057-1075, 2000. ,
Optimal sizes and placements of piezoelectric actuators and sensors for an inflated torus, J. Intell. Mater. Syst. Struct, vol.14, pp.563-576, 2003. ,
Linear Systems, 1980. ,
Vibration control of functionally graded material plate patched with piezoelectric actuators and sensors under a constant electric charge, Smart Mater. Struct, vol.16, pp.1252-1259, 2007. ,
Dynamic analysis and active control of smart doubly curved FGM panels, Compos. Struct, vol.102, pp.205-216, 2013. ,
The positioning of sensors and actuators in the vibration control of flexible systems, JSME Int. J, vol.33, pp.145-152, 1990. ,
Exact frequency equations of free vibration of exponentially functionally graded beams, Appl. Acoust, vol.74, pp.413-420, 2013. ,
The modeling and design of smart structures using functionally graded materials and piezoelectrical sensor/actuator patches, Smart Mater. Struct, vol.12, pp.647-655, 2003. ,
A computational scheme for the optimal sensor/actuator placement of flexible structures using spatial H2 measures, Mech. Syst. Signal Process, vol.20, pp.881-895, 2006. ,
Free vibration of FGM plates with in-plane material inhomogeneity, Compos. Struct, vol.92, pp.1047-1051, 2010. ,
Functionally graded material: an overview, Proceedings of the World Congress on Engineering, p.3, 2012. ,
Review: modeling studies applied to functionally graded materials, J. Mater. Sci, vol.30, pp.2183-2193, 2012. ,
Active control of natural frequencies of FGM plates by piezoelectric sensor/actuator pairs, Smart Mater. Struct, vol.17, p.8, 2008. ,
Exact solution of the bending vibration problem of FGM beams with variation of material properties, Eng. Struct, vol.32, pp.1631-1640, 2010. ,
Modal analysis of the FGM beams with the effect of the shear correction function, Compos. Part B, vol.45, pp.1575-1582, 2013. ,
Optimal sizing and placement of piezo-actuators for active flutter suppression, Smart Mater. Struct, vol.5, pp.2216-2224, 1996. ,
Functionally graded shells with distributed piezoelectric sensors and actuators for active vibration control, IUTAM Symposium on Multi Functional Material Structures and Systems, 2010. ,
Actuator placement optimization and adaptive vibration control of plate smart structures, J. Intell. Mater. Syst. Struct, vol.16, pp.263-271, 2005. ,
Vibration Control of Active Structures, 1999. ,
Optimal placement and active vibration control for piezoelctric smart flexible cantilever plate, J. Sound Vib, vol.301, pp.521-543, 2007. ,
Active vibration control of beams with optimal placement of piezoelectric sensors/ actuator pairs, Smart Mater. Struct, 2008. ,
Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed-fixed boundary condition. Compos, Part B, vol.58, pp.361-370, 2014. ,
Optimal discrete piezoelectric patch allocation on composite structures for vibration control based on GA and modal LQR, Comput. Struct, vol.128, pp.101-115, 2013. ,
Free vibration and stability of axially functionally graded trapered Timoshenko beams with classical and non-classical boundary conditions, Compos. Part B, vol.42, pp.801-808, 2011. ,
Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials, Appl. Math. Model, vol.36, pp.3094-3111, 2012. ,
Active control of functionally graded laminated cylindrical shells, Compos. Struct, vol.90, pp.448-457, 2009. ,
Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load, Compos. Struct, vol.94, pp.2358-2364, 2012. ,
Vibration analyses of FGM plates with in-plane material inhomogeneity by Ritz method, Compos. Struct, vol.94, pp.1398-1405, 2012. ,
A controllability index for optimal design of piezoelectric actuators in vibration control of beam structures, J. Sound Vib, vol.242, issue.3, pp.507-518, 2001. ,
Semi-inverse method for axially functionally graded beams with an anti-symmetric vibration mode, J. Sound Vib, vol.284, pp.1190-1202, 2005. ,
Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction, Compos. Part B, vol.39, pp.292-303, 2008. ,
Optimization of noncollocated sensor/actuator location and feedback gain in control systems, Smart Mater. Struct, vol.2, pp.96-102, 1993. ,
So Integrated optimal design of vibration control system for smart beams using genetic algorithms, J. Sound Vib, vol.282, pp.1293-1307, 2005. ,
Nonlinear dynamic response and active vibration control for piezoelectric functionally graded plate, J. Sound Vib, vol.329, pp.2015-2028, 2010. ,
Active control of piezothermoelastic FGM shells using integrated piezoelectric sensor/ actuator layers, Int. J. Appl. Electromagn. Mech, vol.30, pp.107-124, 2009. ,