]. Insa-lyon-tulkoff and C. , Pad cratering : Prevention, mitigation, and detection strategies, APEX EXPO, 2013.

B. G. Korenev and L. M. Reznikov, Dynamic vibration absorbers: theory and technical applications, 1993.

R. Rana and T. Soong, Parametric study and simplified design of tuned mass dampers. Engineering structures, pp.193-204, 1998.

B. Samali and K. Kwok, Use of viscoelastic dampers in reducing wind-and earthquake-induced motion of building structures. Engineering Structures, pp.639-654, 1995.

D. Niederberger, Smart damping materials using shunt control, p.16043, 2005.

S. Behrens, A. Fleming, and S. Moheimani, A broadband controller for shunt piezoelectric damping of structural vibration. Smart materials and structures, pp.18-28, 2003.

K. Kwok and B. Samali, Performance of tuned mass dampers under wind loads. Engineering Structures, pp.655-667, 1995.

M. Setareh and R. D. Hanson, Tuned Mass Dampers to Control Floor Vibration from Humans, Journal of Structural Engineering, vol.118, issue.3, pp.741-762, 1992.
DOI : 10.1061/(ASCE)0733-9445(1992)118:3(741)

L. Kela and P. Vähäoja, Recent Studies of Adaptive Tuned Vibration Absorbers/Neutralizers, Applied Mechanics Reviews, vol.216, issue.6, pp.62-060801, 2009.
DOI : 10.1016/j.jsv.2006.01.033

J. Zhang, L. He, and E. Wang, A LQR Controller Design for Active Vibration Control of Flexible Structures, 2008 IEEE Pacific-Asia Workshop on Computational Intelligence and Industrial Application, pp.127-132, 2008.
DOI : 10.1109/PACIIA.2008.358

A. G. Wills, D. Bates, and A. J. Fleming, Model Predictive Control Applied to Constraint Handling in Active Noise and Vibration Control, IEEE Transactions on Control Systems Technology, vol.16, issue.1, pp.3-12, 2008.
DOI : 10.1109/TCST.2007.903062

R. L. Wang, H. Gu, and G. Song, Adaptive Robust Sliding Mode Vibration Control of a Flexible Beam Using Piezoceramic Sensor and Actuator: An Experimental Study, Mathematical Problems in Engineering, vol.11, issue.6, pp.20141-20150, 2014.
DOI : 10.1002/rob.4620110602

N. W. Hagood and A. Flotow, Damping of structural vibrations with piezoelectric materials and passive electrical networks, Journal of Sound and Vibration, vol.146, issue.2, pp.243-268, 1991.
DOI : 10.1016/0022-460X(91)90762-9

K. Uchino and T. Ishii, Mechanical Damper Using Piezoelectric Ceramics, Journal of the Ceramic Society of Japan, vol.96, issue.1116, pp.96-863, 1988.
DOI : 10.2109/jcersj.96.863

R. L. Forward, Electronic damping of vibrations in optical structures, Applied Optics, vol.18, issue.5, pp.690-697, 1979.
DOI : 10.1364/AO.18.000690

S. Wu and S. Wu, <title>Piezoelectric shunts with a parallel R-L circuit for structural damping and vibration control</title>, Smart Structures and Materials 1996: Passive Damping and Isolation, pp.259-269, 1996.
DOI : 10.1117/12.239093

A. Baz, Active Control of Periodic Structures, Journal of Vibration and Acoustics, vol.126, issue.4, pp.472-479, 2001.
DOI : 10.1016/0022-460X(88)90226-X

M. Reynolds and S. Daley, Enhancing the band gap of an active metamaterial, Journal of Vibration and Control, vol.1, issue.11, p.1077546315600330, 2015.
DOI : 10.1016/j.physleta.2011.02.044

S. Wu, <title>Method for multiple-mode shunt damping of structural vibration using a single PZT transducer</title>, Smart Structures and Materials 1998: Passive Damping and Isolation, 1998.
DOI : 10.1117/12.310680

J. J. Hollkamp, Multimodal Passive Vibration Suppression with Piezoelectric Materials and Resonant Shunts, Journal of Intelligent Material Systems and Structures, vol.5, issue.1, pp.49-57, 1994.
DOI : 10.1177/1045389X9000100302

S. Behrens, S. R. Moheimani, and A. Fleming, Multiple mode current flowing passive piezoelectric shunt controller, Journal of Sound and Vibration, vol.266, issue.5, pp.929-942, 2003.
DOI : 10.1016/S0022-460X(02)01380-9

A. J. Fleming, S. Behrens, and S. Moheimani, Reducing the inductance requirements of piezoelectric shunt damping systems, Smart Materials and Structures, vol.12, issue.1, pp.57-64, 2003.
DOI : 10.1088/0964-1726/12/1/307

D. Niederberger, A. Fleming, and S. Moheimani, Adaptive multi-mode resonant piezoelectric shunt damping, Smart Materials and Structures, vol.13, issue.5, pp.1025-1035, 2004.
DOI : 10.1088/0964-1726/13/5/007
URL : http://www.eng.newcastle.edu.au/~ajf203/PDFs/J04b.pdf

D. Niederberger, Adaptive resonant shunted piezoelectric devices for vibration suppression Proceedings of SPIE -The International Society for Optical Engineering, pp.213-224, 2003.

J. J. Hollkamp and T. F. Starchville, A Self-Tuning Piezoelectric Vibration Absorber, Journal of Intelligent Material Systems and Structures, vol.5, issue.4, pp.559-566, 1994.
DOI : 10.2514/3.19920

C. L. Davis, G. A. Lesieutre, and J. J. Dosch, Tunable electrically shunted piezoceramic vibration absorber, Proceedings of SPIE -The International Society for Optical Engineering, p.3045, 1997.
DOI : 10.1117/12.274188

C. L. Davis and G. A. Lesieutre, AN ACTIVELY TUNED SOLID-STATE VIBRATION ABSORBER USING CAPACITIVE SHUNTING OF PIEZOELECTRIC STIFFNESS, Journal of Sound and Vibration, vol.232, issue.3, pp.601-617, 2000.
DOI : 10.1006/jsvi.1999.2755

A. Tylikowski, Control of circular plate vibrations via piezoelectric actuators shunted with a capacitive circuit. Thin-Walled Structures, pp.83-94, 2001.

G. A. Lesieutre, Vibration damping and control using shunted piezoelectric materials. The Shock and Vibration Digest, pp.187-195, 1998.
DOI : 10.1177/058310249803000301

C. Richard, <title>Semi-passive damping using continuous switching of a piezoelectric device</title>, Smart Structures and Materials 1999: Passive Damping and Isolation, pp.104-111, 1999.
DOI : 10.1117/12.349773

C. Richard, Enhanced semi-passive damping using continuous switching of a piezoelectric device on an inductor. Proceedings of SPIE -The International Society for, Optical Engineering, vol.3989, pp.104-111, 2000.

C. Richard, D. Guyomar, and E. Lefeuvre, Self-powered electronic breaker with automatic switching by detecting maxima or minima of potential difference between its power electrodes

M. Lallart, É. Lefeuvre, and C. Richard, Self-powered circuit for broadband, multimodal piezoelectric vibration control. Sensors & Actuators A Physical, pp.377-382, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01699468

H. Ji, J. Qiu, and J. Cheng, Application of a Negative Capacitance Circuit in Synchronized Switch Damping Techniques for Vibration Suppression, Journal of Vibration and Acoustics, vol.17, issue.4, pp.41015-41016, 2011.
DOI : 10.1016/j.jsv.2010.01.012

N. S. Shenck and J. A. Paradiso, Energy scavenging with shoe-mounted piezoelectrics, IEEE Micro, vol.21, issue.3, pp.30-42, 2001.
DOI : 10.1109/40.928763

A. J. Insa-lyon-fleming, S. Behrens, and S. R. Moheimani, An autonomous piezoelectric shunt damping system, Proceedings of SPIE-The International Society for Optical Engineering, pp.207-216, 2003.

G. K. Ottman, H. F. Hofmann, and G. A. Lesieutre, Optimized piezoelectric energy harvesting circuit using step-down converter in discontinuous conduction mode, IEEE Transactions on Power Electronics, vol.18, issue.2, pp.1988-1994, 2002.

G. A. Lesieutre, G. K. Ottman, and H. F. Hofmann, Damping as a result of piezoelectric energy harvesting, Journal of Sound and Vibration, vol.269, issue.3-5, pp.991-1001, 2004.
DOI : 10.1016/S0022-460X(03)00210-4

A. J. Fleming, S. Behrens, and S. R. Moheimani, Active LQR and H/sub 2/ shunt control of electromagnetic transducers., 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), pp.2294-2299, 2004.
DOI : 10.1109/CDC.2003.1272960

A. J. Fleming and S. R. Moheimani, Control orientated synthesis of high-performance piezoelectric shunt impedances for structural vibration control, IEEE Transactions on Control Systems Technology, vol.13, issue.1, pp.98-112, 2005.
DOI : 10.1109/TCST.2004.838547

T. Bailey and J. Ubbard, Distributed piezoelectric-polymer active vibration control of a cantilever beam, Journal of Guidance, Control, and Dynamics, vol.26, issue.5, pp.605-611, 1985.
DOI : 10.1016/0016-0032(66)90067-6

M. Hassan, R. Dubay, and C. Li, Active vibration control of a flexible one-link manipulator using a multivariable predictive controller. Mechatronics, pp.17-311, 2007.

G. Takács and B. Roha?-ilkiv, Model Predictive Vibration Control: Efficient Constrained MPC Vibration Control for Lightly Damped Mechanical Structures, 2012.
DOI : 10.1007/978-1-4471-2333-0

J. K. Ji, D. C. Lee, and S. Sul, LQG based speed controller for torsional vibration suppression in 2-mass motor drive system, International Conference on Industrial Electronics, Control, and Instrumentation Proceedings of the IECON. IEEE, pp.1157-1162, 1993.

A. J. Connolly, M. Green, and J. F. Chicharo, The design of LQG and H? controllers for use in active vibration control and narrow band disturbance rejection. Decision and Control, Proceedings of the, IEEE Conference, pp.2982-2987, 1995.

J. Han, K. Rew, and I. Lee, An experimental study of active vibration control of composite structures with a piezo-ceramic actuator and a piezo-film sensor, Smart Materials and Structures, pp.549-558, 1997.
DOI : 10.1088/0964-1726/6/5/006

C. Edwards and S. Spurgeon, Sliding mode control: theory and applications, 1998.

M. Trindade, A. Benjeddou, and R. Ohayon, PIEZOELECTRIC ACTIVE VIBRATION CONTROL OF DAMPED SANDWICH BEAMS, Journal of Sound and Vibration, vol.246, issue.4, pp.653-677, 2001.
DOI : 10.1006/jsvi.2001.3712

T. Yoshimura, A. Kume, and M. Kurimoto, CONSTRUCTION OF AN ACTIVE SUSPENSION SYSTEM OF A QUARTER CAR MODEL USING THE CONCEPT OF SLIDING MODE CONTROL, Journal of Sound and Vibration, vol.239, issue.2, pp.239-187, 2001.
DOI : 10.1006/jsvi.2000.3117

I. R. Petersen and H. R. Pota, Minimax LQG optimal control of a flexible beam, Control Engineering Practice, issue.1111, pp.1273-1287, 2003.

Q. Hu and G. Ma, Variable structure control and active vibration suppression of flexible spacecraft during attitude maneuver, Aerospace Science and Technology, vol.9, issue.4, pp.307-317, 2005.
DOI : 10.1016/j.ast.2005.02.001

V. Utkin, J. Guldner, and J. Shi, Sliding mode control on electro-mechanical systems, Mathematical Problems in Engineering, vol.8, issue.4-5, 2009.
DOI : 10.1080/10241230306724

J. Tang and K. Wang, Active-passive hybrid piezoelectric networks for vibration control: comparisons and improvement, Smart Materials and Structures, vol.10, issue.4, pp.794-806, 2001.
DOI : 10.1088/0964-1726/10/4/325

M. A. Insa-lyon-trindade and A. Benjeddou, Hybrid active-passive damping treatments using viscoelastic and piezoelectric materials: review and assessment, Journal of Vibration and Control, vol.8, issue.6, pp.699-745, 2002.

R. L. Forward, Electromechanical transducer-coupled mechanical structure with negative capacitance compensation circuit: US, US 4158787 A, 1979.

D. R. Browning and W. Wynn, Vibration damping systems using active negative capacitance shunt circuit with piezoelectric reaction mass actuator, The Journal of the Acoustical Society of America, vol.102, issue.6, 1996.
DOI : 10.1121/1.420157

C. H. Park and A. Baz, Vibration Control of Beams with Negative Capacitive Shunting of Interdigital Electrode Piezoceramics, Modal Analysis, vol.9, issue.2, pp.331-346, 2005.
DOI : 10.1177/1045389X9800901204

M. Neubauer, R. Oleskiewicz, and K. Popp, Optimization of damping and absorbing performance of shunted piezo elements utilizing negative capacitance, Journal of Sound and Vibration, vol.298, issue.1-2, pp.84-107, 2006.
DOI : 10.1016/j.jsv.2006.04.043

B. De-marneffe and A. Preumont, Vibration damping with negative capacitance shunts: theory and experiment, Smart Materials and Structures, vol.17, issue.3, pp.17-4006, 2008.
DOI : 10.1088/0964-1726/17/3/035015

R. S. Riordan, Simulated inductors using differential amplifiers, Electronics Letters, vol.3, issue.2, pp.50-51, 1967.
DOI : 10.1049/el:19670039

A. Antoniou, Realisation of gyrators using operational amplifiers, and their use in RC-active-network synthesis, Electrical Engineers Proceedings of the Institution of, pp.116-1838, 1969.
DOI : 10.1049/piee.1969.0339

I. A. Awad and A. Soliman, New CMOS realization of the CCII-, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol.46, issue.4, pp.460-463, 1999.
DOI : 10.1109/82.755417

G. Ferri and N. Guerrini, High-valued passive element simulation using low-voltage low-power current conveyors for fully integrated applications, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol.48, issue.4, pp.48-405, 2001.
DOI : 10.1109/82.933805

W. Clark, Vibration Control with State-Switched Piezoelectric Materials, Journal of Intelligent Material Systems and Structures, vol.11, issue.4, pp.263-271, 2000.
DOI : 10.1115/1.2888213

K. A. Cunefare, S. D. Rosa, and N. Sadegh, State-Switched Absorber for Semi-Active Structural Control, Journal of Intelligent Material Systems and Structures, vol.3045, issue.2, pp.300-310, 2000.
DOI : 10.1177/027836499000900305

G. D. Larson, P. H. Rogers, and W. Munk, State switched transducers: A new approach to high-power, low-frequency, underwater projectors, The Journal of the Acoustical Society of America, vol.103, issue.3, pp.1428-1441, 1998.
DOI : 10.1121/1.421283

A. Ramaratnam, N. Jalili, and D. M. Dawson, Semi-active vibration control using piezoelectric-based switched stiffness, American Control Conference, pp.5461-5466, 2004.

A. Ramaratnam and N. Jalili, A switched stiffness approach for structural vibration control: theory and real-time implementation, Journal of Sound and Vibration, vol.291, issue.1-2, pp.258-274, 2006.
DOI : 10.1016/j.jsv.2005.06.012

A. Lotfi-gaskarimahalle and C. D. Rahn, Switched Stiffness Vibration Controllers for Fluidic Flexible Matrix Composites, Volume 1: 22nd Biennial Conference on Mechanical Vibration and Noise, Parts A and B, 2009.
DOI : 10.1115/DETC2009-87591

H. Shen, J. Qiu, and H. Ji, A low-power circuit for piezoelectric vibration control by synchronized switching on voltage sources. Sensors & Actuators A Physical, pp.245-255, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00503234

H. Ji, J. Qiu, and P. Xia, The influence of switching phase and frequency of voltage on the vibration damping effect in a piezoelectric actuator, Smart Materials and Structures, vol.20, issue.1, pp.15008-15023, 2011.
DOI : 10.1088/0964-1726/20/1/015008

H. Insa-lyon-ji, J. Qiu, and A. Badel, Semi-active Vibration Control of a Composite Beam using an Adaptive SSDV Approach, Journal of Intelligent Material Systems & Structures, issue.20, pp.20-401, 2009.

E. Lefeuvre, A. Badel, and L. Petit, Semi-passive Piezoelectric Structural Damping by Synchronized Switching on Voltage Sources, Journal of Intelligent Material Systems and Structures, vol.17, issue.8-9, pp.17-25, 2006.
DOI : 10.1117/12.384569

A. Badel, G. Sebald, and D. Guyomar, Piezoelectric vibration control by synchronized switching on adaptive voltage sources: Towards wideband semi-active damping, The Journal of the Acoustical Society of America, vol.119, issue.5, pp.119-2815, 2006.
DOI : 10.1121/1.2184149
URL : https://hal.archives-ouvertes.fr/hal-01699424

M. Neubauer, X. Han, and S. Schwarzendahl, Enhanced switching law for synchronized switch damping on inductor with bimodal excitation, Journal of Sound and Vibration, vol.330, issue.12, pp.330-2707, 2011.
DOI : 10.1016/j.jsv.2011.01.003

A. Chérif, C. Richard, and D. Guyomar, Simulation of multimodal vibration damping of a plate structure using a modal SSDI-Max technique, Journal of Intelligent Material Systems and Structures, vol.7288, issue.1, pp.23-675, 2012.
DOI : 10.1117/12.274217

T. Richard, C. Magnet, and C. Richard, Board multimodal vibration control using piezoelectric synchronised switch damping techniques, Journal of Vibration & Control, issue.6, pp.17-845, 2010.
DOI : 10.1177/1077546310362858

J. C. Collinger and J. A. Wickert, Adaptive Piezoelectric Vibration Control With Synchronized Switching, Journal of Dynamic Systems Measurement & Control, issue.131, pp.131-1703, 2009.
DOI : 10.1115/imece2007-41427
URL : http://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1001&context=me_pubs

M. Lallart, S. Harari, and L. Petit, Blind switch damping (BSD): A self-adaptive semi-active damping technique, Journal of Sound and Vibration, vol.328, issue.1-2, pp.29-41, 2009.
DOI : 10.1016/j.jsv.2009.07.030
URL : https://hal.archives-ouvertes.fr/hal-01699671

H. Ji, J. Qiu, and K. Zhu, Two-mode vibration control of a beam using nonlinear synchronized switching damping based on the maximization of converted energy, Journal of Sound and Vibration, vol.329, issue.14, pp.329-2751, 2010.
DOI : 10.1016/j.jsv.2010.01.012

D. Guyomar, C. Richard, and S. Mohammadi, Semi-passive random vibration control based on statistics, Journal of Sound and Vibration, vol.307, issue.3-5, pp.3-5, 2007.
DOI : 10.1016/j.jsv.2007.07.008

A. J. Fleming, S. Behrens, and S. Moheimani, Synthetic impedance for implementation of piezoelectric shunt-damping circuits, Electronics Letters, vol.36, issue.18, pp.36-1525, 2000.
DOI : 10.1049/el:20001083

G. Matten, M. Collet, and S. Cogan, Synthetic Impedance for Adaptive Piezoelectric Metacomposite, Procedia Technology, vol.15, pp.84-89, 2014.
DOI : 10.1016/j.protcy.2014.09.037
URL : https://doi.org/10.1016/j.protcy.2014.09.037

D. J. Warkentin and N. W. Hagood, Nonlinear piezoelectric shunting for structural damping, Smart Structures and Materials' 97. 1997. International Society for Optics and Photonics, pp.747-757

F. Dell-'lsola, D. D. Vescovo, and C. Maurini, Distributed electric absorbers of beam vibrations, Proceedings of SPIE-The International Society for Optical Engineering, pp.230-241, 2003.

F. Dell-'isola, C. Maurini, and M. Porfiri, Passive damping of beam vibrations through distributed electric networks and piezoelectric transducers: prototype design and experimental validation, Smart Materials and Structures, vol.13, issue.2, pp.299-308, 2004.
DOI : 10.1088/0964-1726/13/2/008
URL : https://hal.archives-ouvertes.fr/hal-00496593

C. Maurini, F. Dell-'isola, and D. Vescovo, Comparison of piezoelectronic networks acting as distributed vibration absorbers, Mechanical Systems and Signal Processing, vol.18, issue.5, pp.1243-1271, 2004.
DOI : 10.1016/S0888-3270(03)00082-7
URL : https://hal.archives-ouvertes.fr/hal-00502098

P. Bisegna, G. Caruso, and F. Maceri, Optimized electric networks for vibration damping of piezoactuated beams, Journal of Sound and Vibration, vol.289, issue.4-5, pp.4-5, 2006.
DOI : 10.1016/j.jsv.2005.02.045

I. Giorgio, A. Culla, and D. Vescovo, Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network, Archive of Applied Mechanics, vol.15, issue.5, pp.79-859, 2009.
DOI : 10.1007/s00419-008-0258-x
URL : https://hal.archives-ouvertes.fr/hal-00798627

I. Lyon, M. Aucejo, and J. Deü, Multimodal vibration damping through a periodic array of piezoelectric patches connected to a passive network, 2015.

M. Ruzzene and A. Baz, Control of Wave Propagation in Periodic Composite Rods Using Shape Memory Inserts, Journal of Vibration and Acoustics, vol.118, issue.2, pp.151-159, 2000.
DOI : 10.1021/ja952676d

O. G. Thorp, M. Ruzzene, and A. Baz, Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches, Smart Materials and Structures, vol.10, issue.5, pp.657-696, 2001.
DOI : 10.1088/0964-1726/10/5/314

G. Wang, S. Chen, J. Wen, G. Wang, S. Chen et al., Low-frequency locally resonant band gaps induced by arrays of resonant shunts with Antoniou???s circuit: experimental investigation on beams, Smart Materials and Structures, vol.20, issue.1, p.15026, 2010.
DOI : 10.1088/0964-1726/20/1/015026

L. Airoldi and M. Ruzzene, Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos, New Journal of Physics, vol.13, issue.11, pp.13-746, 2011.
DOI : 10.1088/1367-2630/13/11/113010

G. Wang, J. Wang, and S. Chen, Vibration attenuations induced by periodic arrays of piezoelectric patches connected by enhanced resonant shunting circuits, Smart Materials and Structures, pp.20-125019, 2011.
DOI : 10.1088/0964-1726/20/12/125019

S. Chen, G. Wang, and J. Wen, Wave propagation and attenuation in plates with periodic arrays of shunted piezo-patches, Journal of Sound and Vibration, vol.332, issue.6, pp.332-1520, 2013.
DOI : 10.1016/j.jsv.2012.11.005

A. Bergamini, T. Delpero, and L. D. Simoni, Phononic Crystal with Adaptive Connectivity, Advanced Materials, vol.116, issue.9, pp.1343-1347
DOI : 10.1049/piee.1969.0339

G. Wang and S. Chen, Large low-frequency vibration attenuation induced by arrays of piezoelectric patches shunted with amplifier???resonator feedback circuits, Smart Materials and Structures, vol.25, issue.1, pp.25-015004, 2016.
DOI : 10.1088/0964-1726/25/1/015004

B. Beck, K. A. Cunefare, and M. Ruzzene, Broadband Vibration Suppression Assessment of Negative Impedance Shunts, Smart Materials, Adaptive Structures and Intelligent Systems, Volume 1, pp.491-500, 2008.
DOI : 10.1115/SMASIS2008-535

Y. Y. Chen, G. L. Huang, and C. Sun, Band Gap Control in an Active Elastic Metamaterial With Negative Capacitance Piezoelectric Shunting, Journal of Vibration and Acoustics, vol.136, issue.6, p.136, 2014.
DOI : 10.1115/1.4028378

T. Huang, M. Ichchou, and M. Collet, Wave propagation control in smart structures with shunted piezoelectric patches Design variables for optimizing adaptive metacomposite made of shunted piezoelectric patches distribution Experimental characterization of a bi-dimensional array of negative capacitance piezo-patches for vibroacoustic control, ISMA 2012 conference on Noise and Vibration Engineering. 2012. [104], pp.1045389-14536006, 2014.

F. Casadei, B. S. Beck, and K. A. Cunefare, Vibration control of plates through hybrid configurations of periodic piezoelectric shunts, Journal of Intelligent Material Systems and Structures, vol.11, issue.10, pp.23-1169, 2012.
DOI : 10.1177/1077546309106529

H. Zhang, J. Wen, and S. Chen, Flexural wave band-gaps in phononic metamaterial beam with hybrid shunting circuits, Chinese Physics B, vol.24, issue.3, pp.24-269, 2015.
DOI : 10.1088/1674-1056/24/3/036201

. Lyon, Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication, 2016.

M. Lallart, L. Yan, and C. Richard, Damping of periodic bending structures featuring nonlinearly interfaced piezoelectric elements, Journal of Vibration and Control, vol.9, issue.18
DOI : 10.1177/1045389X13493355

I. De-lyon-guyomar, D. Badel, and A. , Nonlinear semi-passive multimodal vibration damping: An efficient probabilistic approach, Journal of Sound and Vibration, vol.294, issue.1-2, pp.249-268, 2006.
DOI : 10.1016/j.jsv.2005.11.010

M. Lallart, C. Magnet, and C. Richard, New Synchronized Switch Damping methods using dual transformations. Sensors and Actuators A: Physical, pp.302-314, 2008.
DOI : 10.1016/j.sna.2007.12.001
URL : https://hal.archives-ouvertes.fr/hal-01699470

J. B. Pendry, A. J. Holden, and W. J. Stewart, Extremely Low Frequency Plasmons in Metallic Mesostructures, Physical Review Letters, vol.50, issue.25, pp.76-4773, 1996.
DOI : 10.1103/PhysRevB.50.5062

Y. A. Vlasov, X. Z. Bo, and J. C. Sturm, On-chip natural assembly of silicon photonic bandgap crystals, Nature, vol.410, issue.6861, pp.414-289, 2001.
DOI : 10.1038/35065571

L. Brillouin, Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices

J. Lee, J. P. Singer, and E. Thomas, Micro-/Nanostructured Mechanical Metamaterials, Advanced Materials, vol.106, issue.36, pp.24-4782
DOI : 10.1103/PhysRevLett.106.214503

Z. Liu, X. Zhang, and Y. Mao, Locally Resonant Sonic Materials, Science, vol.289, issue.5485, pp.1734-1736, 2000.
DOI : 10.1126/science.289.5485.1734

B. Sharma and C. Sun, Local resonance and Bragg bandgaps in sandwich beams containing periodically inserted resonators, Journal of Sound and Vibration, vol.364, issue.364, pp.133-146, 2016.
DOI : 10.1016/j.jsv.2015.11.019

L. Dai, S. Jiang, and Z. Lian, Locally resonant band gaps achieved by equal frequency shunting circuits of piezoelectric rings in a periodic circular plate, Journal of Sound and Vibration, vol.337, pp.150-160, 2015.
DOI : 10.1016/j.jsv.2014.10.026

Y. Xiao, J. Wen, and G. Wang, Theoretical and Experimental Study of Locally Resonant and Bragg Band Gaps in Flexural Beams Carrying Periodic Arrays of Beam-Like Resonators, Journal of Vibration and Acoustics, vol.135, issue.4, p.41006, 2013.
DOI : 10.1115/1.4024214

Y. Xiao, J. Wen, and X. Wen, Broadband locally resonant beams containing multiple periodic arrays of attached resonators, Physics Letters A, vol.376, issue.16, pp.376-1384
DOI : 10.1016/j.physleta.2012.02.059

Y. Xiao, J. Wen, and D. Yu, Flexural wave propagation in beams with periodically attached vibration absorbers: Band-gap behavior and band formation mechanisms, Journal of Sound and Vibration, vol.332, issue.4, pp.867-893, 2013.
DOI : 10.1016/j.jsv.2012.09.035

C. Croënne, L. E. Hu, and H. , Band gaps in phononic crystals: Generation mechanisms and interaction effects, AIP Advances, vol.84, issue.4, p.41401, 2011.
DOI : 10.1038/nphys1101

F. M. Li, Y. S. Wang, and C. Hu, Localization of elastic waves in randomly disordered multi-coupled multi-span beams. Waves in random media, pp.14-217, 2004.

D. Bouzit and C. Pierre, Wave localization and conversion phenomena in multi-coupled multi-span beams, Chaos, Solitons & Fractals, vol.11, issue.10, pp.11-1575, 2000.
DOI : 10.1016/S0960-0779(99)00079-X

O. Bendiksen, Mode localization phenomena in large space structures, AIAA Journal, vol.91, issue.9, pp.1241-1248, 1987.
DOI : 10.1016/B978-0-444-85315-8.50006-2

. Lyon, Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication, 2016.

M. Collet, K. A. Cunefare, and M. Ichchou, Wave Motion Optimization in Periodically Distributed Shunted Piezocomposite Beam Structures, Journal of Intelligent Material Systems and Structures, vol.341, issue.12, pp.20-787, 2009.
DOI : 10.1006/jsvi.1995.0153

M. Collet, M. Ouisse, and M. Ichchou, Semi-Active Optimization of 2D Wave???s Dispersion Into Shunted Piezocomposite Systems for Controlling Acoustic Interaction, ASME 2011 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, Volume 1, pp.79-87, 2011.
DOI : 10.1115/SMASIS2011-5018

M. Collet, M. Ouisse, and M. Ichchou, Structural energy flow optimization through adaptive shunted piezoelectric metacomposites, Journal of Intelligent Material Systems and Structures, vol.11, issue.7, pp.23-1661
DOI : 10.1016/j.jsv.2008.05.039

T. L. Huang, M. N. Ichchou, and O. A. Bareille, Traveling wave control in thin-walled structures through shunted piezoelectric patches, Mechanical Systems and Signal Processing, vol.39, issue.1-2, pp.59-79, 2013.
DOI : 10.1016/j.ymssp.2012.06.014

T. Huang, M. N. Ichchou, and O. Bareille, Multimodal wave propagation in smart composite structures with shunted piezoelectric patches Structural multi-modal damping by optimizing shunted piezoelectric transducers, Journal of Intelligent Material Systems and Structures European Journal of Computational Mechanics, pp.20-21, 2011.

K. Yamada, H. Matsuhisa, and H. Utsuno, Enhancement of efficiency of vibration suppression using piezoelectric elements and LR circuit by amplification of electrical resonance, Journal of Sound and Vibration, vol.333, issue.5, pp.333-1281
DOI : 10.1016/j.jsv.2013.10.001

L. Airoldi, M. Ruzzene, B. R. Mace, and M. Brennan, Wave propagation control in beams through periodic multi-branch shunts Finite element analysis of the vibrations of waveguides and periodic structures, Journal of Intelligent Material Systems and Structures Journal of sound and vibration, issue.1, pp.294-205, 2006.

L. Houillon, M. N. Ichchou, and L. Jezequel, Wave motion in thin-walled structures, Journal of Sound and Vibration, vol.281, issue.3-5, pp.281-483, 2005.
DOI : 10.1016/j.jsv.2004.01.020

B. R. Mace, D. Duhamel, and M. J. Brennan, Finite element prediction of wave motion in structural waveguides, The Journal of the Acoustical Society of America, vol.117, issue.5, pp.2835-2843, 2005.
DOI : 10.1121/1.1887126

M. N. Ichchou, J. M. Mencik, and W. Zhou, Wave finite elements for low and mid-frequency description of coupled structures with damage. Computer methods in applied mechanics and engineering, pp.198-1311, 2009.

J. M. Mencik and M. Ichchou, Multi-mode propagation and diffusion in structures through finite elements, European Journal of Mechanics - A/Solids, vol.24, issue.5, pp.24-877, 2005.
DOI : 10.1016/j.euromechsol.2005.05.004

V. R. Challa, M. G. Prasad, and Y. Shi, A vibration energy harvesting device with bidirectional resonance frequency tunability, ): 015035. [142] Beranek L L, Ver I L. Noise and vibration control engineering-principles and applications, 2008.
DOI : 10.1088/0964-1726/17/01/015035

G. H. Koopmann, D. J. Fox, and W. Neise, Active source cancellation of the blade tone fundamental and harmonics in centrifugal fans, Journal of Sound and Vibration, vol.126, issue.2, pp.126-209, 1988.
DOI : 10.1016/0022-460X(88)90236-2

D. Karnopp, Active and Semi-Active Vibration Isolation, Journal of Vibration and Acoustics, vol.5, issue.B, pp.177-185, 1995.
DOI : 10.1115/1.3591760

N. S. Khot, V. B. Venkayya, and F. Eastep, Optimal structural modifications to enhance the active vibration control of flexible structures, AIAA Journal, vol.80, issue.8, pp.24-1368, 1986.
DOI : 10.1007/BF01588967

P. A. Deymier, S. Noda, K. Tomoda, and N. Yamamoto, Acoustic metamaterials and phononic crystals Springer Science & Business Media Full three-dimensional photonic bandgap crystals at near-infrared wavelengths, Science, vol.173149, issue.5479, pp.289-604, 2000.

W. Zhou, Y. Wu, and L. Zuo, Vibration and wave propagation attenuation for metamaterials by periodic piezoelectric arrays with high-order resonant circuit shunts, Smart Materials and Structures, vol.24, issue.6, pp.24-065021
DOI : 10.1088/0964-1726/24/6/065021

M. G. Soto and H. Adeli, Tuned mass dampers, Archives of Computational Methods in Engineering, vol.2013, issue.204, pp.419-431

P. Bonello, A. Vonflotow, A. Beard, and D. Bailey, Adaptive tuned vibration absorbers: design principles, concepts and physical implementation Adaptive tuned vibration absorbers: tuning laws, tracking agility, sizing, and physical implementations.Noise Con, Proceedings of the 1994 National Conference on Noise Control Engineering, pp.437-454, 1994.
DOI : 10.5772/23558
URL : http://www.intechopen.com/download/pdf/17683

M. J. Brennan and J. Dayou, GLOBAL CONTROL OF VIBRATION USING A TUNABLE VIBRATION NEUTRALIZER, Journal of Sound and Vibration, vol.232, issue.3
DOI : 10.1006/jsvi.1999.2757

M. J. Brennan, Vibration control using a tunable vibration neutralizer Proceedings of the Institution of Mechanical Engineers, Journal of Mechanical Engineering Science, issue.2, pp.211-91, 1997.

H. Frahm, Device for damping vibrations of bodies: U.S. Patent 989, pp.958-1911

J. Ormondroyd, Theory of the dynamic vibration absorber. Transaction of the ASME, pp.9-22, 1928.

M. Kidner and M. Brennan, IMPROVING THE PERFORMANCE OF A VIBRATION NEUTRALISER BY ACTIVELY REMOVING DAMPING, Journal of Sound and Vibration, vol.221, issue.4, pp.587-606, 1999.
DOI : 10.1006/jsvi.1998.2027

L. Zuo and S. A. Nayfeh, Minimax optimization of multi-degree-of-freedom tuned-mass dampers, Journal of Sound and Vibration, vol.272, issue.3-5
DOI : 10.1016/S0022-460X(03)00500-5

L. Zuo and S. A. Nayfeh, Optimization of the Individual Stiffness and Damping Parameters in Multiple-Tuned-Mass-Damper Systems, Journal of Vibration and Acoustics, vol.31, issue.1, pp.77-83, 2005.
DOI : 10.1115/1.1855929

G. C. Marano and G. Quaranta, Robust optimum criteria for tuned mass dampers in fuzzy environments, Applied Soft Computing, vol.9, issue.4, pp.1232-1243, 2009.
DOI : 10.1016/j.asoc.2009.03.010

L. Zuo, Effective and Robust Vibration Control Using Series Multiple Tuned-Mass Dampers, Journal of Vibration and Acoustics, vol.118, issue.3
DOI : 10.1121/1.414545

O. Tigli, Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads, Journal of Sound and Vibration, vol.331, issue.13, pp.331-3035
DOI : 10.1016/j.jsv.2012.02.017

G. C. Marano, R. Greco, and B. Chiaia, A comparison between different optimization criteria for tuned mass dampers design, Journal of Sound and Vibration, issue.23, pp.329-4880, 2010.

. Lyon, Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication, 2016.

N. Hoang, Y. Fujino, and P. Warnitchai, Optimal tuned mass damper for seismic applications and practical design formulas. Engineering structures, pp.707-715, 2008.

G. Bekda? and S. Nigdeli, Estimating optimum parameters of tuned mass dampers using harmony search, Engineering Structures, vol.33, issue.9, pp.2716-2723, 2011.
DOI : 10.1016/j.engstruct.2011.05.024

D. Hrovat, P. Barak, and M. Rabins, Semi???Active versus Passive or Active Tuned Mass Dampers for Structural Control, Journal of Engineering Mechanics, vol.109, issue.3, pp.691-705, 1983.
DOI : 10.1061/(ASCE)0733-9399(1983)109:3(691)

K. Fujii, Y. Tamura, and T. Sato, Wind-induced vibration of tower and practical applications of tuned sloshing damper, Journal of Wind Engineering and Industrial Aerodynamics, vol.33, issue.1-2, pp.263-272, 1990.
DOI : 10.1016/0167-6105(90)90042-B

T. Balendra, C. M. Wang, and H. Cheong, Effectiveness of tuned liquid column dampers for vibration control of towers. Engineering Structures, pp.17-668, 1995.

N. Jalili and I. Knowles, Structural vibration control using an active resonator absorber: modeling and control implementation, Smart Materials and Structures, vol.13, issue.5, pp.998-1005, 2004.
DOI : 10.1088/0964-1726/13/5/004

P. Bonello, M. J. Brennan, and S. J. Elliott, Designs for an adaptive tuned vibration absorber with variable shape stiffness element, Proceedings of the Royal Society
DOI : 10.1098/rspa.2005.1547

S. M. Kim, S. Wang, and M. Brennan, Dynamic analysis and optimal design of a passive and an active piezo-electrical dynamic vibration absorber, Journal of Sound and Vibration, vol.330, issue.4, pp.603-614, 2011.
DOI : 10.1016/j.jsv.2010.09.004

M. H. Tso, J. Yuan, and W. Wong, Suppression of random vibration in flexible structures using a hybrid vibration absorber, Journal of Sound and Vibration, vol.331, issue.5, pp.331-974
DOI : 10.1016/j.jsv.2011.10.017

A. Kareem and S. Kline, Performance of Multiple Mass Dampers under Random Loading, Journal of Structural Engineering, vol.121, issue.2, pp.348-361, 1995.
DOI : 10.1061/(ASCE)0733-9445(1995)121:2(348)

P. Bonello, M. J. Brennan, and S. Elliott, Vibration control using an adaptive tuned vibration absorber with a variable curvature stiffness element, Smart Materials and Structures, vol.14, issue.5, pp.14-1055, 2005.
DOI : 10.1088/0964-1726/14/5/044

F. Weber, C. Boston, and M. Ma?lanka, An adaptive tuned mass damper based on the emulation of positive and negative stiffness with an MR damper, Smart Materials and Structures, vol.20, issue.1, 2010.
DOI : 10.1088/0964-1726/20/1/015012

K. Jr and E. M. , Damping of flexural waves by a constrained viscoelastic layer, The Journal of the Acoustical society of America, issue.7, pp.31-952, 1959.

D. Ross, E. E. Ungar, and E. Kerwin, Damping of plate flexural vibrations by means of viscoelastic laminae. Structural damping, pp.44-87, 1959.

A. K. Lall, N. T. Asnani, and B. Nakra, Damping analysis of partially covered sandwich beams, Journal of Sound and Vibration, vol.123, issue.2
DOI : 10.1016/S0022-460X(88)80109-3

S. W. Kung and R. Singh, VIBRATION ANALYSIS OF BEAMS WITH MULTIPLE CONSTRAINED LAYER DAMPING PATCHES, Journal of Sound and Vibration, vol.212, issue.5, pp.781-805, 1998.
DOI : 10.1006/jsvi.1997.1409

B. Nakra, VIBRATION CONTROL IN MACHINES AND STRUCTURES USING VISCOELASTIC DAMPING, Journal of Sound and Vibration, vol.211, issue.3, pp.449-466, 1998.
DOI : 10.1006/jsvi.1997.1317

S. W. Kung and R. Singh, DEVELOPMENT OF APPROXIMATE METHODS FOR THE ANALYSIS OF PATCH DAMPING DESIGN CONCEPTS, Journal of Sound and Vibration, vol.219, issue.5, pp.785-812, 1999.
DOI : 10.1006/jsvi.1998.1876

Y. C. Hu and S. Huang, The frequency response and damping effect of three-layer thin shell with viscoelastic core, Computers & Structures, vol.76, issue.5, pp.76-577, 2000.
DOI : 10.1016/S0045-7949(99)00182-0

. Lyon, Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication, 2016.

D. Jones, Response and damping of a simple beam with tuned dampers. The journal of the acoustical society of America, pp.50-53, 1967.

M. D. Rao, Recent applications of viscoelastic damping for noise control in automobiles and commercial airplanes, Journal of Sound and Vibration, vol.262, issue.3, pp.457-474, 2003.
DOI : 10.1016/S0022-460X(03)00106-8

A. Rashid and C. Nicolescu, Design and implementation of tuned viscoelastic dampers for vibration control in milling, International Journal of Machine Tools and Manufacture, vol.48, issue.9, pp.48-1036, 2008.
DOI : 10.1016/j.ijmachtools.2007.12.013

H. Ghoneim, <title>Electromechanical surface damping using constrained layer and shunted piezoelectric</title>, Smart Structures and Materials 1993: Mathematics in Smart Structures, pp.78-89, 1993.
DOI : 10.1117/12.148431

C. H. Park and A. Baz, VIBRATION CONTROL OF BENDING MODES OF PLATES USING ACTIVE CONSTRAINED LAYER DAMPING, Journal of Sound and Vibration, vol.227, issue.4, pp.711-734, 1999.
DOI : 10.1006/jsvi.1999.2391

C. Chantalakhana and R. Stanway, ACTIVE CONSTRAINED LAYER DAMPING OF CLAMPED-CLAMPED PLATE VIBRATIONS, Journal of Sound and Vibration, vol.241, issue.5, pp.241-755, 2001.
DOI : 10.1006/jsvi.2000.3317

M. C. Ray and A. Baz, Control of Nonlinear Vibration of Beams Using Active Constrained Layer Damping, Journal of Vibration and Control, vol.5, issue.4, pp.539-549, 2001.
DOI : 10.1115/1.2930434

Z. Xu, M. Y. Wang, and T. Chen, Particle damping for passive vibration suppression: numerical modelling and experimental investigation, Journal of Sound and Vibration, vol.279, issue.3-5, pp.279-1097, 2005.
DOI : 10.1016/j.jsv.2003.11.023

T. M. Yasuda-k, The Damping Effect of an Impact Damper, Bulletin of JSME, vol.21, issue.153, pp.424-430, 1978.
DOI : 10.1299/jsme1958.21.424

S. Ema and E. Marui, A fundamental study on impact dampers, International Journal of Machine Tools and Manufacture, vol.34, issue.3, pp.407-421, 1994.
DOI : 10.1016/0890-6955(94)90009-4

A. S. Butt and F. A. Akl, Numerical Model of Impact-Damped Continuous Systems, Journal of Engineering Mechanics, vol.123, issue.4, pp.384-392, 1997.
DOI : 10.1061/(ASCE)0733-9399(1997)123:4(384)

A. Papalou and S. Masri, An Experimental Investigation of Particle Dampers Under Harmonic Excitation, Journal of Vibration and Control, vol.28, issue.241, pp.361-379, 1998.
DOI : 10.1016/0022-460X(89)90922-X

C. J. Wu, W. H. Liao, and M. Wang, Modeling of Granular Particle Damping Using Multiphase Flow Theory of Gas-Particle, Journal of Vibration and Acoustics, vol.165, issue.2, pp.196-201, 2004.
DOI : 10.1115/1.1688763

W. Liu, G. R. Tomlinson, and J. A. Rongong, The dynamic characterisation of disk geometry particle dampers, Journal of Sound and Vibration, vol.280, issue.3-5, pp.280-849, 2005.
DOI : 10.1016/j.jsv.2003.12.047

K. S. Marhadi and V. Kinra, Particle impact damping: effect of mass ratio, material, and shape, Journal of Sound and Vibration, vol.283, issue.1-2
DOI : 10.1016/j.jsv.2004.04.013

X. M. Bai, L. M. Keer, and Q. J. Wang, Investigation of particle damping mechanism via particle dynamics simulations, Granular Matter, vol.26, issue.Part 1, pp.11-417, 2009.
DOI : 10.1103/PhysRevE.64.051302

R. D. Friend and V. Kinra, PARTICLE IMPACT DAMPING, Journal of Sound and Vibration, vol.233, issue.1, pp.93-118, 2000.
DOI : 10.1006/jsvi.1999.2795

S. Masri, General Motion of Impact Dampers, The Journal of the Acoustical Society of America, vol.47, issue.1B
DOI : 10.1121/1.1911470

C. Saluena, T. Poeschel, and S. Esipov, Dissipative properties of vibrated granular materials, Physical Review E, vol.79, issue.4
DOI : 10.1103/PhysRevLett.79.833

A. Papalou and S. Masri, Response of impact dampers with granular materials under random excitation. Earthquake engineering & structural dynamics, pp.25-253, 1996.

. Lyon, Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication, 2016.

J. M. Mcelhaney, A. Palazzolo, and A. Kascak, Modeling and Simulation Methods for MDOF Structures and Rotating Machinery With Impact Dampers, Journal of Engineering for Gas Turbines and Power, vol.119, issue.2, pp.436-446, 1995.
DOI : 10.1115/1.2815594

N. Popplewell and S. Semercigil, Performance of the bean bag impact damper for a sinusoidal external force, Journal of Sound and Vibration, vol.133, issue.2, pp.193-223, 1989.
DOI : 10.1016/0022-460X(89)90922-X

C. Cempel and G. Lotz, Efficiency of Vibrational Energy Dissipation by Moving Shot, Journal of Structural Engineering, vol.119, issue.9, pp.2642-2652, 1993.
DOI : 10.1061/(ASCE)0733-9445(1993)119:9(2642)

K. Mao, M. Y. Wang, and Z. Xu, DEM simulation of particle damping, Powder Technology, vol.142, issue.2-3, pp.154-165, 2004.
DOI : 10.1016/j.powtec.2004.04.031

K. D. Weiss, J. D. Carlson, and D. Nixon, Viscoelastic Properties of Magneto- and Electro-Rheological Fluids, Journal of Intelligent Material Systems and Structures, vol.5, issue.6, pp.772-775, 1994.
DOI : 10.1177/1045389X9300400103

R. Stanway, J. L. Sproston, and N. Stevens, Non-linear modelling of an electro-rheological vibration damper, Journal of Electrostatics, vol.20, issue.2, pp.167-184, 1987.
DOI : 10.1016/0304-3886(87)90056-8

R. Stanway, J. L. Sproston, and A. Elwahed, Applications of electro-rheological fluids in vibration control: a survey, Smart Materials and Structures, vol.5, issue.4, pp.464-482, 1996.
DOI : 10.1088/0964-1726/5/4/011

M. Sasaki, T. Ishii, and K. Haji, Electro rheological fluid: U.S. Patent 5, pp.280-1997

A. Khanicheh, D. Mintzopoulos, and B. Weinberg, Evaluation of Electrorheological Fluid Dampers for Applications at 3-T MRI Environment, IEEE/ASME Transactions on Mechatronics, vol.13, issue.3, pp.286-294, 2008.
DOI : 10.1109/TMECH.2008.924043

M. R. Jolly, J. D. Carlson, and B. Muñoz, A model of the behaviour of magnetorheological materials, Smart Materials and Structures, vol.5, issue.5, pp.607-614, 1996.
DOI : 10.1088/0964-1726/5/5/009

S. J. Dyke, B. F. Spencer, and M. K. Sain, Modeling and control of magnetorheological dampers for seismic response reduction, Smart Materials and Structures, vol.5, issue.5, pp.565-575, 1996.
DOI : 10.1088/0964-1726/5/5/006

J. De-vicente, D. J. Klingenberg, and R. Hidalgo-alvarez, Magnetorheological fluids: a review, Soft Matter, vol.82, issue.3, pp.7-3701, 2011.
DOI : 10.1103/PhysRevLett.82.233

J. D. Carlson, D. M. Catanzarite, . St, and K. Clair, COMMERCIAL MAGNETO-RHEOLOGICAL FLUID DEVICES, International Journal of Modern Physics B, vol.10, issue.23n24
DOI : 10.1142/S0217979296001306

O. Ashour, C. A. Rogers, and W. Kordonsky, Magnetorheological fluids: materials, characterization, and devices. Journal of intelligent material systems and structures, pp.123-130, 1996.
DOI : 10.1177/1045389x9600700201

D. Damjanovic and R. Newnham, Electrostrictive and piezoelectric materials for actuator applications Journal of intelligent material systems and structures, pp.190-208, 1992.

J. Galvagni, Electrostrictive actuators and their use in optical applications, Optical Engineering, vol.29, issue.11, pp.1389-1391, 1990.
DOI : 10.1117/12.55742

M. Lallart, L. Wang, and C. Richard, Lumped model of bending electrostrictive transducers for energy harvesting, Journal of Applied Physics, vol.116, issue.12, pp.116-124106
DOI : 10.1121/1.1377291

F. Lee, Modeling of actuator systems using multilayer electrostrictive materials, Proceedings of the 1999 IEEE International Conference on. IEEE, pp.1406-1411, 1999.

Y. Liu, K. L. Ren, and H. F. Hofmann, Investigation of electrostrictive polymers for energy harvesting, ieee transactions on ultrasonics, ferroelectrics, and frequency control, issue.12, pp.52-2411, 2005.

. Lyon, Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication, 2016.

L. Wang, M. Lallart, and L. Petit, Low-cost charge of electrostrictive polymers for efficient energy harvesting, Journal of Intelligent Material Systems and Structures, vol.26, issue.16, pp.26-2123
DOI : 10.1063/1.1446035

G. Song, N. Ma, and H. Li, Applications of shape memory alloys in civil structures. Engineering structures, pp.28-1266, 2006.

K. Otsuka and C. D. Wayman, Shape memory materials Shape memory alloys, Science and Business Media LLC, vol.228, 1999.

D. J. Hartl and D. Lagoudas, Aerospace applications of shape memory alloys, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol.253, issue.6, pp.535-552, 2007.
DOI : 10.1016/S0020-7225(98)00116-5

A. Baz, K. Imam, and J. Mccoy, Active vibration control of flexible beams using shape memory actuators, Journal of Sound and Vibration, vol.140, issue.3, pp.140-437, 1990.
DOI : 10.1016/0022-460X(90)90760-W

F. Auricchio and R. L. Taylor, Shape-memory alloys: modelling and numerical simulations of the finite-strain superelastic behavior Computer methods in applied mechanics and engineering, pp.175-194, 1997.

H. Block, J. P. Kelly, and A. Qin, Materials and mechanisms in electrorheology, Langmuir, vol.6, issue.1, 1990.
DOI : 10.1021/la00091a002

A. Tonoli, M. Silvagni, and N. Amati, Electromechanical Dampers for Vibration Control of Structures and Rotors, 2010.
DOI : 10.5772/10040

H. A. Sodano, J. S. Bae, and D. J. Inman, Concept and model of eddy current damper for vibration suppression of a beam, Journal of Sound and Vibration, vol.288, issue.4-5, pp.1177-1196, 2005.
DOI : 10.1016/j.jsv.2005.01.016

J. Meisel, Principles of electromechanical-energy conversion, 1984.

H. Y. Kim and C. Lee, Design and control of active magnetic bearing system with Lorentz force-type axial actuator, Mechatronics, vol.16, issue.1, pp.13-20, 2006.
DOI : 10.1016/j.mechatronics.2005.09.005

J. S. Bae, J. H. Hwang, and D. G. Kwag, Vibration Suppression of a Large Beam Structure Using Tuned Mass Damper and Eddy Current Damping, Shock and Vibration, vol.54, issue.55, pp.20141-20151, 2014.
DOI : 10.1007/s11803-012-0129-x

D. G. Fink, A. Mckenzie, K. E. Graves, D. Toncich, and P. Iovenitti, Electronics engineers' handbook Theoretical comparison of motional and transformer EMF device damping efficiency, Journal of Sound and Vibration, issue.3, pp.233-441, 1975.

K. Nagaya and H. Kojima, On a Magnetic Damper Consisting of a Circular Magnetic Flux and a Conductor of Arbitrary Shape. Part I: Derivation of the Damping Coefficients, Journal of Dynamic Systems, Measurement, and Control, vol.106, issue.1, pp.46-51, 1984.
DOI : 10.1115/1.3149662

T. Ikeda, Fundamentals of piezoelectricity, 1996.

B. Jaffe, Piezoelectric Ceramics, Journal of the American Ceramic Society, vol.36, issue.11, 2012.
DOI : 10.1143/JPSJ.7.333

H. Olson, Electronic control of noise, vibration, and reverberation. The Journal of the

G. S. Agnes and K. Napolitano, ACTIVE CONSTRAINED LAYER VISCOELASTIC DAMPING, 34th Structures, Structural Dynamics and Materials Conference
DOI : 10.2514/6.1993-1702

B. Azvine, G. R. Tomlinson, and R. Wynne, Use of active constrained-layer damping for controlling resonant vibration, Smart Materials and Structures, vol.4, issue.1, pp.1-6, 1995.
DOI : 10.1088/0964-1726/4/1/001

. Lyon, Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication, 2016.

M. J. Lam, D. J. Inman, and W. Saunders, Vibration Control through Passive Constrained Layer Damping and Active Control, Journal of Intelligent Material Systems and Structures, vol.3045, issue.34, pp.663-677, 1997.
DOI : 10.1115/1.2930434

M. J. Lam, D. J. Inman, and W. Saunders, Variations of hybrid damping, 5th Annual International Symposium on Smart Structures and Materials. International Society for Optics and Photonics, pp.32-43, 1998.

P. Horowitz, W. Hill, and I. Robinson, The art of electronics, 1980.

S. Y. Wu, Broadband piezoelectric shunts for structural vibration control: U.S. Patent 6,075, pp.309-2000
DOI : 10.1117/12.432708

D. Guyomar, M. Lallart, and T. Monnier, Innovative vibration control systems based on smart materials for light structures. Diss. Italy Stiffness tuning using a low-cost semiactive nonlinear technique, IEEE/ASME Transactions on Mechatronics, vol.252, issue.5, pp.13-604, 2008.

M. Lallart, A. Badel, and D. Guyomar, Nonlinear Semi-active Damping using Constant or Adaptive Voltage Sources: A Stability Analysis, Journal of Intelligent Material Systems and Structures, vol.128, issue.2, pp.191131-1142, 2008.
DOI : 10.1117/12.384569
URL : https://hal.archives-ouvertes.fr/hal-01699498

D. Niederberger and M. Morari, An autonomous shunt circuit for vibration damping, Smart Materials and Structures, vol.15, issue.2, pp.359-364, 2006.
DOI : 10.1088/0964-1726/15/2/016

H. Ji, J. Qiu, and P. Xia, Coupling analysis of energy conversion in multi-mode vibration structural control using a synchronized switch damping method Comment onAcoustic band structure of periodic elastic composites, Smart Materials and Structures, pp.15013-75, 1995.

M. Sigalas and E. Economou, Band structure of elastic waves in two dimensional systems, Solid State Communications, vol.86, issue.3, pp.141-143, 1993.
DOI : 10.1016/0038-1098(93)90888-T

T. T. Wu, Z. G. Huang, and T. C. Tsai, Evidence of complete band gap and resonances in a plate with periodic stubbed surface, 111902. [260] Maldovan, M., Narrow low-frequency spectrum and heat management by thermocrystals, p.93, 2008.
DOI : 10.1121/1.418423

E. N. Economou and M. Sigalas, Stop bands for elastic waves in periodic composite materials, The Journal of the Acoustical Society of America, vol.95, issue.4, pp.1734-1740, 1994.
DOI : 10.1121/1.408692

M. S. Kushwaha and P. Halevi, Band???gap engineering in periodic elastic composites, Applied Physics Letters, vol.38, issue.9, pp.1085-1087, 1994.
DOI : 10.1109/58.67833

M. M. Sigalas and E. Economou, Elastic waves in plates with periodically placed inclusions, Journal of Applied Physics, vol.158, issue.6
DOI : 10.1103/PhysRevLett.69.3080

. Lyon, Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication, 2016.

W. H. Bragg and W. Bragg, The reflection of X-rays by crystals, Containing Papers of a Mathematical and Physical Character, pp.88-428, 1913.

D. Yu, J. Wen, and H. Zhao, Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid, Journal of Sound and Vibration, vol.318, issue.1-2, pp.318-193, 2008.
DOI : 10.1016/j.jsv.2008.04.009

M. Kafesaki, E. Economou, D. García-pablos, M. Sigalas, and F. Espinosa, Multiple-scattering theory for three-dimensional periodic acoustic composites. Physical review B Theory and experiments on elastic band gaps, Physical Review Letters, vol.60268, issue.1719, pp.11993-844349, 1999.

P. Langlet, A. Hladky?hennion, and J. Decarpigny, Analysis of the propagation of plane acoustic waves in passive periodic materials using the finite element method, The Journal of the Acoustical Society of America, vol.98, issue.5, pp.98-2792, 1995.
DOI : 10.1121/1.413244

G. Wang, X. Wen, and J. Wen, Two-Dimensional Locally Resonant Phononic Crystals with Binary Structures, Physical Review Letters, vol.52, issue.15, pp.939587-9602, 2004.
DOI : 10.1103/PhysRevB.28.1711

C. Goffaux, J. Sánchez-dehesa, and A. L. Yeyati, Evidence of fano-like interference phenomena in locally resonant materials. Physical review letters, pp.88-225502, 2002.

G. Wang, D. Yu, and J. Wen, One-dimensional phononic crystals with locally resonant structures, Physics Letters A, vol.327, issue.5-6, pp.327-512, 2004.
DOI : 10.1016/j.physleta.2004.05.047

G. Wang, X. Wen, and J. Wen, Quasi-One-Dimensional Periodic Structure with Locally Resonant Band Gap, Journal of Applied Mechanics, vol.268, issue.1, pp.167-170, 2006.
DOI : 10.1016/S0022-460X(02)01629-2

S. Vidoli and F. Dell-'isola, Modal coupling in one-dimensional electromechanical structured continua, Acta Mechanica, vol.35, issue.1-2, pp.37-50, 2000.
DOI : 10.1007/978-1-4612-3584-2
URL : https://hal.archives-ouvertes.fr/hal-00501520

C. C. Fuller, S. Elliott, and P. Nelson, Active control of vibration, 1996.

Y. Kim and A. Baz, Active control of a two-dimensional periodic structure, Smart Structures and Materials 2004: Damping and Isolation, pp.329-339, 2004.
DOI : 10.1117/12.540672

F. Li and Z. Song, Vibration analysis and active control of nearly periodic two-span beams with piezoelectric actuator/sensor pairs, Applied Mathematics and Mechanics, vol.302, issue.3, pp.36-279
DOI : 10.1016/j.jsv.2006.06.080

M. S. Rao and S. Narayanan, Active control of wave propagation in multi-span beams using distributed piezoelectric actuators and sensors, Smart Materials & Structures, issue.6, pp.162577-2594, 2007.

A. Singh, D. J. Pines, and A. Baz, Active/passive reduction of vibration of periodic one-dimensional structures using piezoelectric actuators, Smart Materials and Structures, vol.13, issue.4, pp.698-711, 2004.
DOI : 10.1088/0964-1726/13/4/007

C. Hansen, S. Snyder, and X. Qiu, Active control of noise and vibration Active vibration control of smart piezoelectric beams, 2012.

M. Collet, Y. Fan, and M. Ichchou, Periodically distributed piezoelectric patches optimization for waves attenuation and vibrations damping, The Journal of the Acoustical Society of America, vol.138, issue.3, pp.1920-1920, 2015.
DOI : 10.1121/1.4934042

T. L. Huang, M. N. Ichchou, and O. A. Bareille, Multi-modal wave propagation in smart structures with shunted piezoelectric patches, Computational Mechanics, vol.181, issue.3, pp.52-721, 2013.
DOI : 10.1006/jsvi.1995.0153
URL : https://hal.archives-ouvertes.fr/hal-00993372

. Lyon, Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication, 2016.

J. Wen, S. Chen, and G. Wang, Directionality of wave propagation and attenuation in plates with resonant shunting arrays Hybrid dispersive media with controllable wave propagation: A new take on smart materials, Journal of Intelligent Material Systems and Structures Journal of Applied Physics, vol.2014286287, issue.15, pp.118-154310, 2015.

S. Degraeve, C. Granger, and B. Dubus, Bragg band gaps tunability in an homogeneous piezoelectric rod with periodic electrical boundary conditions Tunable effective constants of the one-dimensional piezoelectric phononic crystal with internal connected electrodes, Journal of applied Physics The Journal of the Acoustical Society of America, vol.2014288, issue.1152, pp.137-606, 2015.

J. M. Mencik and M. Ichchou, A substructuring technique for finite element wave propagation in multi-layered systems, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.6-8, pp.197-505, 2008.
DOI : 10.1016/j.cma.2007.08.002

J. Becker, O. Fein, and M. Maess, Finite element-based analysis of shunted piezoelectric structures for vibration damping, Computers & Structures, vol.84, issue.31-32, pp.84-2340, 2006.
DOI : 10.1016/j.compstruc.2006.08.067

D. J. Mead, A general theory of harmonic wave propagation in linear periodic systems with multiple coupling, Journal of Sound and Vibration, vol.27, issue.2, pp.235-260, 1973.
DOI : 10.1016/0022-460X(73)90064-3

D. Mead, Wave propagation and natural modes in periodic systems: I. Mono-coupled systems, Journal of Sound and Vibration, vol.40, issue.1, pp.1-18, 1975.
DOI : 10.1016/S0022-460X(75)80227-6

W. X. Zhong and F. Williams, On the direct solution of wave propagation for repetitive structures, Journal of Sound and Vibration, vol.181, issue.3, pp.181-485, 1995.
DOI : 10.1006/jsvi.1995.0153

Z. Hao, W. Ji-hong, and C. Sheng-bing, Flexural wave band-gaps in phononic metamaterial beam with hybrid shunting circuits Broadband attenuation in Phononic Beams induced by periodic arrays of feedback shunted piezoelectric patches, Chinese Physics Letters, pp.36201-36230, 2012.

C. Sheng-bing, W. Ji-hong, and Y. Dian-long, Band gap control of phononic beam with negative capacitance piezoelectric shunt Locally resonant gaps of phononic beams induced by periodic arrays of resonant shunts, Chinese Physics Letters, pp.14301-14329, 2011.

G. Wang, S. Chen, and J. Wen, Low-frequency locally resonant band gaps induced by arrays of resonant shunts with Antoniou???s circuit: experimental investigation on beams, Smart Materials and Structures, vol.20, issue.1, p.15026, 2010.
DOI : 10.1088/0964-1726/20/1/015026

Y. W. Kwon and H. Bang, The finite element method using MATLAB, 2000.

L. Cesari, Functional analysis and Galerkin's method., The Michigan Mathematical Journal, vol.11, issue.4, pp.385-414, 1964.
DOI : 10.1307/mmj/1028999194

H. Allik and T. Hughes, Finite element method for piezoelectric vibration, International Journal for Numerical Methods in Engineering, vol.37, issue.2, pp.151-157, 1970.
DOI : 10.1109/T-SU.1968.29457

F. Casadei, M. Ruzzene, and L. Dozio, Broadband vibration control through periodic arrays of resonant shunts: experimental investigation on plates. Smart materials and structures, p.15002, 2009.

. Lyon, Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication, 2016.

A. Spadoni, M. Ruzzene, and K. Cunefare, Vibration and Wave Propagation Control of Plates with Periodic Arrays of Shunted Piezoelectric Patches, Journal of Intelligent Material Systems and Structures, vol.9, issue.12, pp.20-979, 2009.
DOI : 10.1088/0964-1726/5/5/017

H. S. Tzou and C. Tseng, Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: A piezoelectric finite element approach, Journal of Sound and Vibration, vol.138, issue.1
DOI : 10.1016/0022-460X(90)90701-Z

L. Yan, M. Lallart, and D. Guyomar, Hybrid time-domain and spatial filtering nonlinear damping strategy for efficient broadband vibration control, Journal of Intelligent Material Systems and Structures, vol.9, issue.157, pp.261-277
DOI : 10.1177/1045389X13493355

T. Kaneko, On Timoshenko's correction for shear in vibrating beams, Journal of Physics D: Applied Physics, vol.8, issue.16
DOI : 10.1088/0022-3727/8/16/003

Z. Friedman and J. Kosmatka, An improved two-node timoshenko beam finite element, Computers & Structures, vol.47, issue.3
DOI : 10.1016/0045-7949(93)90243-7

H. Ji, J. Qiu, and K. Zhu, Vibration control of a composite beam by an adaptive semi-active method based on LMS algorithm, Piezoelectricity, Acoustic Waves, and Device Applications, 2008.

J. Park, D. Palumbo, N. S. Bardell, R. S. Langley, and J. M. Dunsdon, A new approach to identify optimal properties of shunting elements for maximum damping of structural vibration using piezoelectric patches. INTER-NOISE and NOISE-CON Congress and Conference Proceedings The effect of period asymmetry on wave propagation in periodic beams, Journal of sound and vibration, vol.197, issue.4, pp.427-445, 1996.

Y. Aköz and M. Aksoydan, Transfer Stiffnes Matrix for Timoshenko Beams on Elastic Foundations

S. T. Wei and C. Pierre, Statistical analysis of the forced response of mistuned cyclic assemblies, AIAA Journal, vol.28, issue.5
DOI : 10.1115/1.3149532

M. N. Ichchou, S. Akrout, and J. Mencik, Guided waves group and energy velocities via finite elements, Journal of Sound and Vibration, vol.305, issue.4-5, pp.931-944, 2007.
DOI : 10.1016/j.jsv.2007.05.007

L. Insa-lyon, B. Yan, D. Bao, M. Guyomar, and . Lallart, Periodic Structure with Interconnected Nonlinear Electrical Networks, these.pdf © [B. Bao], [2016], 2016.

B. Bao, D. Guyomar, and M. Lallart, Vibration reduction for smart periodic structures via periodic piezoelectric arrays with nonlinear interleaved-switched electronic networks, Mechanical Systems and Signal Processing, vol.82
DOI : 10.1016/j.ymssp.2016.05.021

B. Bao, D. Guyomar, and M. Lallart, Electron???phonon metamaterial featuring nonlinear tri-interleaved piezoelectric topologies and its application in low-frequency vibration control, Smart Materials and Structures, vol.25, issue.9
DOI : 10.1088/0964-1726/25/9/095010

B. Bao, M. Lallart, and D. Guyomar, Nonlinear Vibration Damping in Mechanical/Electrical Periodic Structures Featuring Switched Piezoelectric Elements, th International Conference on Smart and Multifunctional Materials, Structures and Systems, CIMTEC 2016, Session E-1 -Physics and Modelling of Metamaterials Systems, 2016.

. Prénoms, Bin TITRE : Systèmes de contrôle de vibrations distribué large bande utilisant des approches non-linéaires NATURE : Doctorat Numéro d'ordre, pp.2016-086

E. Ecole-doctorale:-electronique and A. Spécialité, augmentation du niveau de sécurité des structures requièrent le développement de techniques permettant de limiter efficacement les vibrations. Dans cette optique, les travaux exposés ici proposent le développement et l'analyse de méthodes de contrôle vibratoire pour des structures de faibles dimensions et utilisant peu d'énergie Afin de satisfaire à ces deux critères, il est ici proposé d'utiliser des éléments piézoélectriques électriquement interfacés de manière non-linéaire et périodiquement distribués sur la structure-cible à contrôler. Ainsi, l'approche proposée permet de bénéficier à la fois des avantages des techniques de contrôle non-linéaires appliquées aux matériaux intelligents de type piézoélectrique, offrant des performances remarquables tout en étant peu consommatrices d'énergie, avec ceux des structures périodiques exhibant des bandes fréquentielles interdites présentant de fortes atténuations de la propagation d'onde. Plus particulièrement, ce mémoire s'intéresse à différentes architectures d'interconnexion des interfaces électriques non-linéaires permettant un bon compromis entre la bande fréquentielle contrôlée et les performances en termes d'atténuation des vibrations. Ainsi, trois architectures principales sont proposées, impactant ainsi la propagation de l'onde acoustique en élargissant la bande de contrôle, pour enfin proposer une architecture hybride entre interconnexion et entrelacement conduisant à des systèmes large bande performants