M. S. Rao and S. Narayanan, Active control of wave propagation in multi-span beams using distributed piezoelectric actuators and sensors, Smart Materials and Structures, vol.16, p.2577, 2007.

L. Ding, H. Zhu, and T. Yin, Wave propagation in a periodic elastic-piezoelectric axial-bending coupled beam, Journal of Sound and Vibration, vol.332, pp.6377-6388, 2013.

O. 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, p.979, 2001.

S. Chen, J. Wen, G. Wang, D. Yu, and X. Wen, Improved modeling of rods with periodic arrays of shunted piezoelectric patches, Journal of Intelligent Material Systems and Structures, vol.23, pp.1613-1621, 2012.

O. Thorp, M. Ruzzene, and A. Baz, Attenuation of wave propagation in fluid-loaded shells with periodic shunted piezoelectric rings, Smart Materials and Structures, vol.14, p.594, 2005.

L. Airoldi and M. Ruzzene, Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos, New Journal of Physics, vol.13, p.113010, 2011.

L. Airoldi and M. Ruzzene, Wave propagation control in beams through periodic multi-branch shunts, Journal of Intelligent Material Systems and Structures, vol.22, pp.1567-1579, 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, p.15026, 2011.

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, p.65021, 2015.

S. Chen and G. Wang, Wave propagation in beams with anti-symmetric piezoelectric shunting arrays, Chinese Physics B, vol.25, p.34301, 2016.

G. Wang, J. Wang, S. Chen, and J. Wen, Vibration attenuations induced by periodic arrays of piezoelectric patches connected by enhanced resonant shunting circuits, Smart Materials and Structures, vol.20, p.125019, 2011.

H. Zhang, J. Wen, S. Chen, G. Wang, and X. Wen, Flexural wave band-gaps in phononic metamaterial beam with hybrid shunting circuits, Chinese Physics B, vol.24, p.36201, 2015.

M. Lallart, L. Yan, C. Richard, and D. Guyomar, Damping of periodic bending structures featuring nonlinearly interfaced piezoelectric elements, Journal of Vibration and Control, vol.22, pp.3930-3941, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01769149

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, pp.230-259, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02165405

M. Collet, K. A. Cunefare, and M. N. Ichchou, Wave motion optimization in periodically distributed shunted piezocomposite beam structures, Journal of Intelligent Material Systems and Structures, vol.20, pp.787-808, 2009.

Y. Fan, M. Collet, M. Ichchou, L. Li, O. Bareille et al., A wave-based design of semi-active piezoelectric composites for broadband vibration control, Smart Materials and Structures, vol.25, p.55032, 2016.

D. J. Mead, Wave propagation in continuous periodic structures: research contribution from southampton, Journal of Sound and Vibration, vol.190, pp.495-524, 1964.

B. R. Mace, D. Duhamel, M. J. Brennan, and L. Hinke, Finite element prediction of wave motion in structural waveguides, The Journal of the Acoustical Society of America, vol.117, pp.2835-2843, 2005.

D. Duhamel, B. Mace, and M. Brennan, Finite element analysis of the vibrations of waveguides and periodic structures, Journal of Sound and Vibration, vol.294, pp.205-220, 2006.

J. Mencik, On the low-and mid-frequency forced response of elastic structures using wave finite elements with onedimensional propagation, Computers & Structures, vol.88, pp.674-689, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00755757

P. B. Silva, J. Mencik, and J. R. De-franca-arruda, Wave finite element-based superelements for forced response analysis of coupled systems via dynamic substructuring, International Journal for Numerical Methods in Engineering, vol.107, pp.453-476, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01709691

T. L. Huang, M. N. Ichchou, O. A. Bareille, M. Collet, and M. Ouisse, Traveling wave control in thin-walled structures through shunted piezoelectric patches, Mechanical Systems and Signal Processing, vol.39, pp.59-79, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00993396

Y. Fan, M. Collet, M. Ichchou, L. Li, O. Bareille et al., Enhanced wave and finite element method for wave propagation and forced response prediction in periodic piezoelectric structures, Chinese Journal of Aeronautics, vol.30, pp.75-87, 2017.

O. Thomas, J. Deü, and J. Ducarne, Vibrations of an elastic structure with shunted piezoelectric patches: efficient finite element formulation and electromechanical coupling coefficients, International Journal for Numerical Methods in Engineering, vol.80, pp.235-268, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01572491

B. Lossouarn, M. Aucejo, and J. Deü, Multimodal coupling of periodic lattices and application to rod vibration damping with a piezoelectric network, Smart Materials and Structures, vol.24, p.45018, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01691077

B. Lossouarn, J. F. Deü, and M. Aucejo, Multimodal vibration, Smart Materials and Structures, vol.24, p.115037, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01691077

A. E. Bergamini, M. Zündel, E. A. Flores-parra, T. Delpero, M. Ruzzene et al., Hybrid dispersive media with controllable wave propagation: A new take on smart materials, vol.118, p.154310, 2015.

E. A. Parra, A. Bergamini, B. V. Damme, and P. Ermanni, Controllable wave propagation of hybrid dispersive media with lc high-pass and band-pass networks, Applied Physics Letters, vol.110, p.184103, 2017.

Y. Lu and J. Tang, Electromechanical tailoring of structure with periodic piezoelectric circuitry, Journal of Sound and Vibration, vol.331, pp.3371-3385, 2012.

L. Yan, B. Bao, D. Guyomar, and M. Lallart, Periodic structure with interconnected nonlinear electrical networks, Journal of Intelligent Material Systems and Structures, pp.1045389-16649448, 2016.
URL : https://hal.archives-ouvertes.fr/hal-02112491

B. Bao, D. Guyomar, and M. Lallart, Piezoelectric metacomposite structure carrying nonlinear multilevel interleavedinterconnected switched electronic networks, Composite Structures, vol.161, pp.308-329, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02165389

J. Deü, B. Lossouarn, and M. Aucejo, Comparison of electromechanical transfer matrix models for passive damping involving an array of shunted piezoelectric patches, Proceedings of the 22nd International Congress on Sound and Vibration, 2015.

B. Lossouarn, M. Aucejo, and J. Deü, Transverse wave propagation in a one-dimensional structure coupled to its electrical analogue: Comparison of transfer matrix models, Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01739657

B. Lossouarn, M. Aucejo, and J. Deü, Wave finite element method for electromechanical periodic waveguides, Proceedings of the 8th ECCOMAS Thematic Conference on Smart Structures and Materials, SMART 2017, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01739786

G. Horner and W. Pilkey, The riccati transfer matrix method, Journal of Mechanical Design, vol.100, pp.297-302, 1978.

X. Huiyn, A combined dynamic finite element-riccati transfer matrix method for solving non-linear eigenproblems of vibrations, Computers & Structures, vol.53, pp.1257-1261, 1994.

H. Xue, A combined finite element-riccati transfer matrix method in frequency domain for transient structural response, Computers & Structures, vol.62, pp.215-220, 1997.

N. Stephen, On the riccati transfer matrix method for repetitive structures, Mechanics Research Communications, vol.37, pp.663-665, 2010.

S. Nanthakumar, T. Lahmer, X. Zhuang, H. S. Park, and T. Rabczuk, Topology optimization of piezoelectric nanostructures, Journal of the Mechanics and Physics of Solids, vol.94, pp.316-335, 2016.

S. Nanthakumar, T. Lahmer, X. Zhuang, G. Zi, and T. Rabczuk, Detection of material interfaces using a regularized level set method in piezoelectric structures, Inverse Problems in Science and Engineering, vol.24, pp.153-176, 2016.

A. Bloch, Electromechanical analogies and their use for the analysis of mechanical and electromechanical systems, Journal of the Institution of Electrical Engineers -Part I: General, vol.92, pp.157-169, 1945.

W. X. Zhong and F. W. Williams, On the direct solution of wave propagation for repetitive structures, Journal of Sound and Vibration, vol.181, pp.485-501, 1995.

C. Maurini, F. Isola, and D. D. Vescovo, Comparison of piezoelectronic networks acting as distributed vibration absorbers, Mechanical Systems and Signal Processing, vol.18, pp.124-1271, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00502098

L. Brillouin, Wave propagation in periodic structures, 1946.

B. Lossouarn, Multimodal vibration damping of structures coupled to their analogous piezoelectric networks, Theses, Conservatoire national des arts et metiers -CNAM, 2016.

M. Porfiri, F. Isola, and F. M. Mascioli, Circuit analog of a beam and its application to multimodal vibration damping, using piezoelectric transducers, International Journal of Circuit Theory and Applications, vol.32, pp.167-198, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00499413

B. Lossouarn, M. Aucejo, J. De, and K. A. Cunefare, Design of a passive electrical analogue for piezoelectric damping of a plate, Journal of Intelligent Material Systems and Structures, vol.0, pp.1045389-17731232
URL : https://hal.archives-ouvertes.fr/hal-01739210