, Ce schéma a pour but d'assurer trois fonctions principales : (i) commander le pot vibrant afin que ce dernier impose au prototype une accélération sinusoïdale d'amplitude constante égale à 5 m.s ?2 (pour ce faire il est possible de jouer manuellement sur la constante "Const_acc_V" jusqu'à ce que l'accélération mesurée corresponde à la valeur souhaitée et ce, à chaque changement de fréquence) ; (ii) automatiser l'acquisition des mesures provenant des différents capteurs. Les grandeurs modifiables en temps réel par l'utilisateur (à l'aide du logiciel ControleDesk) sont détaillées dans le Tableau A.1. Le bloc "gene_sin_cont" génère un signal Figure A.1 -Schéma Simulink pour l, Le schéma Simulink détaillé en Figure A.1 a été utilisé pour l'asservissement du banc expérimental aux Chapitres 2 et 3 lors de l'étude des comportements sous-harmoniques du géné-rateur bistable

. Bibliographie,

B. Rashid and B. H. Rehmani, Applications of wireless sensor networks for urban areas : A survey, Journal of Network and Computer Applications, vol.60, pp.192-219, 2016.

. Oneprod,

M. T. Penella, J. Albesa, and M. Gasulla, Powering wireless sensor nodes : Primary batteries versus energy harvesting, International Instrumentation and Measurement Technology Conference, pp.5-7, 2009.

A. Gutiérrez, C. Gonzàlez, J. Jiménez-leube, S. Zazo, N. Dopico et al., A Heterogeneous Wireless Identification Network for the Localization of Animals Based on Stochastic Movements, Sensors, vol.9, pp.3942-3957, 2009.

, Pile lithium/ion primaire energizer l91. data.energizer.com/pdfs/l91.pdf

J. A. Paradiso and T. Starner, Energy scavenging for mobile and wireless electronics, IEEE Pervasive computing, vol.4, pp.18-27, 2005.
DOI : 10.1109/mprv.2005.9

. Wikipédia,

, Wikipédia (ressources et consommation énergétiques mondiales

. Wikipédia,

S. Basagni, M. Y. Naderi, C. Petrioli, and D. Spenza, Wirless Sensor Networks With Energy Harvesting, Mobile Ad Hoc Networking, vol.20, pp.701-736, 2013.

H. Sharma, A. Haque, and Z. Jaffery, Solar energy harvesting wireless sensor network nodes : A survey, Journal of Renewable and Sustainable Energy, vol.10, p.23704, 2018.

D. Champier, Thermoelectric generators : A review of applications. Energy Conversion and Management, vol.140, pp.167-181, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02014514

C. B. Williams and R. B. Yates, Analysis Of A Micro-electric Generator For Microsystems, Sensors and Actuators A : Physical, vol.52, pp.8-11, 1996.

, Pi (manufacturer of precision motion systems

. Supermagnete,

S. Roundy, P. K. Wright, and J. Rabaey, A study of low level vibrations as a power source for wireless sensor nodes, Computer Communication, vol.26, pp.1131-1144, 2003.

J. Siang, M. H. Lim, and M. S. Leong, Review of vibration-based energy harvesting technology : Mechanism and architectural approach, International Journal of Energy Research, pp.1-28, 2018.

M. F. Daqaq, R. Masana, A. Erturk, and D. D. Quinn, On the role of nonlinearities in vibratory energy harvesting : A critical review and discussion, Applied Mechanics Reviews, vol.66, p.40801, 2014.

R. L. Harne and K. W. Wang, A review of the recent research on vibration energy harvesting via bistable systems, Smart Materials and Structures, vol.22, p.23001, 2013.

J. Kymissis, C. Kendall, J. Paradiso, and N. Gershenfeld, Parasitic power harvesting in shoes, Digest of Papers. Second International Symposium on Wearable Computers, pp.9-10, 1998.

J. Granstrom, J. Feenstra, H. A. Sodano, and K. Farinholt, Energy harvesting from a backpack instrumented with piezoelectric shoulder straps, Smart Materials and Structures, vol.16, pp.1810-1820, 2007.

S. Pobering, N. Ebermeyer, and N. Schwesinger, Generation of electrical energy using short piezoelectric cantilevers in flowing media, Proc. SPIE 7288, Active and Passive Smart Structures and Integrated Systems, 2009.

S. Priya, Modeling of electric energy harvesting using piezoelectric windmill, Applied Physics Letters, vol.87, p.184101, 2005.

M. Pozzi and M. Zhu, Plucked Piezoelectric Bimorphs for Knee-joint Energy Harvesting : Modelling and Experimental Validation, Smart Materials and Structures, vol.20, p.55007, 2011.

E. Arroyo, A. Badel, F. Formosa, Y. P. Wu, and J. Qiu, Comparison of electromagnetic and piezoelectric vibration energy harvesters : Model and experiments, Sensors and Actuators A : Physical, vol.183, pp.148-156, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00782490

S. Roundy and P. K. Wright, A piezoelectric vibration based generator, Smart Materials and Structures, vol.13, pp.1131-1142, 2004.

A. Badel and E. Lefeuvre, Wideband Piezoelectric Energy Harvester Tuned Through its Electronic Interface Circuit, Journal of Physics : Conference Series, vol.557, p.12115, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01322280

. Midé,

S. M. Shahruz, Design of mechanical band-pass filters for energy scavenging, Journal of Sound and Vibration, vol.292, pp.987-998, 2006.

G. Zhang and J. Hu, A Branched Beam-Based Vibration Energy Harvester, Journal of Electronic Materials, vol.43, pp.3912-3921, 2014.

B. Ahmed-seddik, G. Despesse, S. Boisseau, and E. Defay, Self-powered resonant frequency tuning for Piezoelectric Vibration Energy Harvesters, Journal of Physics : Conference Series, vol.476, p.12069, 2013.

A. Badel and E. Lefeuvre, Wideband Piezoelectric Energy Harvester Tuned Through its Electronic Interface Circuit, Journal of Physics : Conference Series, vol.557, p.12115, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01322280

Y. Cai and Y. Manoli, System Design of A Time-Controlled Broadband Piezoelectric Energy Harvesting Interface Circuit, IEEE International Symposium on Circuits and Systems, pp.24-27, 2015.

A. Morel, R. Grézaud, G. Pillonnet, P. Gasnier, G. Despesse et al., Active AC / DC control for wideband piezoelectric energy harvesting, Journal of Physics : Conference Series, vol.773, p.12059, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01574297

A. Morel, G. Pillonnet, Y. Wanderoild, and A. Badel, Dielectric Losses Considerations for Piezoelectric Energy Harvesting, Journal of Low Power Electronics, vol.14, pp.244-254, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01865139

B. P. Mann and N. D. Sims, Energy Harvesting from the Nonlinear Oscillations of Magnetic Levitation, Journal of Sound and Vibration, vol.319, pp.515-530, 2009.

D. A. Barton, S. G. Burrow, and L. R. Clare, Energy Harvesting From Vibrations With a Nonlinear Oscillator, Journal of Vibration and Acoustics, vol.132, p.21009, 2010.

R. Masana and M. F. Daqaq, Electromechanical Modeling and Nonlinear Analysis of Axially Loaded Energy Harvesters, Journal of Vibration and Acoustics, vol.133, p.11007, 2011.

C. Lan, L. Tang, and W. Qinh, Obtaining high-energy responses of nonlinear piezoelectric energy harvester by voltage impulse perturbations, European Physical Journal Applied Physics, vol.79, pp.1-15, 2017.

A. Erturk and D. J. Inman, Broadband piezoelectric power generation on high-energy orbits of the bistable duffing oscillator with electromechanical coupling, Journal of Sound and Vibration, vol.330, pp.2339-2353, 2011.

S. C. Stanton, C. C. Mcgehee, and B. P. Mann, Nonlinear dynamics for broadband energy harvesting : Investigation of a bistable piezoelectric inertial generator, Physica D, vol.239, pp.640-653, 2010.

W. Q. Liu, A. Badel, F. Formosa, Y. P. Wu, N. Bencheikh et al., A wideband integrated piezoelectric bistable generator : Experimental performance evaluation and potential for real environmental vibrations, Journal of Intelligent Material Systems and Structures, vol.26, pp.872-877, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01322281

W. Yang and S. Towfighian, A Hybrid Nonlinear Vibration Energy Harvester. Mechanical Systems and Signal Processing, vol.90, pp.317-333, 2017.

S. Zhou, J. Cao, W. Wang, S. Liu, and J. Lin, Modeling and experimental verification of doubly nonlinear magnet-coupled piezoelectric energy harvesting from ambient vibration, Smart Materials and Structures, vol.24, p.55008, 2015.

S. Zhou, J. Cao, D. J. Inman, J. Lin, S. Liu et al., Broadband tristable energy harvester : Modeling and experiment verification, Applied Energy, vol.133, pp.33-39, 2014.

D. Alghisi, S. Dalola, M. Ferrari, and V. Ferrari, Triaxial Ball-Impact Piezoelectric Converter for Autonomous Sensors Exploiting Energy Harvesting from Vibrations and Human Motion, Sensors & Actuators : A. Physical, vol.233, pp.569-581, 2015.

Y. P. Wu, A. Badel, F. Formosa, W. Q. Liu, and A. Agbossou, Nonlinear vibration energy harvesting device integrating mechanical stoppers used as synchronous mechanical switches, Journal of Intelligent Material Systems and Structures, vol.25, pp.1658-1663, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01322279

Z. Lin, J. Chen, X. Li, J. Li, J. Liu et al., Broadband and threedimensional vibration energy harvesting by a non-linear magnetoelectric generator, Applied Physics Letters, vol.109, p.253903, 2016.

C. Richard, D. Guyomar, D. Audigier, and H. Bassaler, Enhanced semi passive damping using continuous switching of a piezoelectric device on an inductor, Proceedings of SPIE : Smart Structures and Materials, vol.3989, pp.288-299, 2000.

D. Guyomar, A. Badel, E. Lefeuvre, and C. Richard, Toward Energy Harvesting Using Active Materials and Conversion Improvement by Nonlinear Processing, IEEE transactions on ultrasonics, ferroelectrics, and frequency control, vol.52, pp.584-595, 2005.

D. Guyomar and M. Lallart, Recent Progress in Piezoelectric Conversion and Energy Harvesting Using Nonlinear Electronic Interfaces and Issues in Small Scale Implementation, vol.2, pp.274-294, 2011.

W. Q. Liu, Conception d'un dispositif de récupération d'energie vibratoire large bande, 2014.

W. Q. Liu, A. Badel, F. Formosa, Y. P. Wu, and A. Agbossou, Novel piezoelectric bistable oscillator architecture for wideband vibration energy harvesting, Smart Materials and Structures, vol.22, p.35013, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00782337

W. Q. Liu, A. Badel, F. Formosa, and Y. P. Wu, A new figure of merit for wideband vibration energy harvesters, Smart Materials and Structures, vol.24, p.125012, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01322274

G. Sebald, H. Kuwano, D. Guyomar, and B. Ducharne, Experimental duffing oscillator for broadband piezoelectric energy harvesting, Smart Materials and Structures, vol.20, p.102001, 2011.

G. Sebald, H. Kuwano, D. Guyomar, and B. Ducharne, Simulation of a duffing oscillator for broadband piezoelctric energy harvesting, Smart Materials and Structures, vol.20, p.75022, 2011.

Y. Wu, A. Badel, F. Formosa, W. Liu, and A. Agbossou, Piezoelectric vibration energy harvesting by optimized synchronous electric charge extraction, Journal of Intelligent Material Systems and Structures, vol.24, pp.1445-1458, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00782484

G. Duffing and . Buchbesprechungen, Zeitschrift für Angewandte Mathematik und Mechanik, Journal of Applied Mathematics and Mechanics), vol.1, pp.72-73, 1921.

S. P. Pellegrini, N. Tolou, M. Schenk, and J. L. Herder, Bistable vibration energy harvesters : A review, Journal of Intelligent Material Systems and Structures, vol.24, pp.1303-1312, 2013.

F. C. Moon and S. W. Shaw, Chaotic vibrations of a beam with non-linear boundary conditions, Non-linear Mechanics, vol.18, pp.465-477, 1983.

S. A. Emam and A. H. Nayfeh, Nonlinear responses of buckled beams to subharmonic resonance excitations, Nonlinear Dynamics, vol.35, pp.105-122, 2004.

A. F. Arrieta, S. A. Neild, and D. J. Wagg, Nonlinear dynamic response and modeling of a bi-stable composite plate for applications to adaptive structures, Nonlinear Dynamics, vol.58, pp.259-272, 2009.

S. N. Mahmoodi, N. Jalili, and M. Ahmadian, Subharmonics analysis of nonlinear flexural vibrations of piezoelectrically actuated microcantilevers, Nonlinear Dynamics, vol.59, pp.397-409, 2010.

A. F. Arrieta, P. Hagedorn, A. Erturk, and D. J. Inman, A piezoelectric bistable plate for nonlinear broadband energy harvesting, Applied Physics Letters, vol.97, p.104102, 2010.

A. Syta, G. Litak, M. I. Friswell, and S. Adhikari, Multiple solutions and corresponding power output of nonlinear piezoelectric energy harvesters, The European Physical Journal B, vol.89, p.99, 2016.

, Theory of Ordinary Differential Equations. Tata McGraw-Hill Education, 1955.

G. Floquet, Sur les équations différentielles linéaires à coefficients périodiques, Annales scientifiques de l'ENS, vol.12, pp.47-88, 1883.

R. L. Harne, M. Thota, and K. W. Wang, Concise and high-fidelity predictive criteria for maximizing performance and robustness of bistable energy harvesters, Applied Physics Letters, vol.102, p.53903, 2013.
DOI : 10.1063/1.4790381

F. Cottone, P. Basset, H. Vocca, L. Gammaitoni, and T. Bourouina, Bistable electromagnetic generator based on buckled beams for vibrationn energy harvesting, Journal of Intelligent Material Systems and Structures, vol.25, pp.1484-1495, 2014.
DOI : 10.1177/1045389x13508330

R. L. Harne and Q. Dai, Characterizing the robustness and susceptibility of steady-state dynamics in post-buckled structures to stochastic perturbations, Journal of Sound and Vibration, vol.395, pp.258-271, 2017.

R. Masana and M. F. Daqaq, Energy harvesting in the super-harmonic frequency region of a twin-well oscillator, Journal of Applied Physics, vol.111, p.44501, 2012.

W. Y. Tseng and J. Dugundji, Nonlinear Vibrations of a Buckled Beam Under Harmonic Excitation, Journal of Applied Mechanics, vol.37, pp.292-297, 1971.
DOI : 10.1115/1.3408799

M. I. Friswell, S. F. Ali, O. Bilgen, S. Adhikari, A. W. Lees et al., Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass, Journal of Intelligent Material Systems and Structures, vol.23, pp.1505-1521, 2012.

T. Huguet, A. Badel, and M. Lallart, Exploiting bistable oscillator subharmonics for magnified broadband vibration energy harvesting, Applied Physics Letters, vol.111, p.173905, 2017.
DOI : 10.1063/1.5001267

URL : https://hal.archives-ouvertes.fr/hal-01764325

T. Huguet, A. Badel, O. Druet, and M. Lallart, Drastic bandwidth enhancement of bistable energy harvesters : Study of subharmonic behaviors and their stability robustness, Applied Energy, vol.226, pp.607-617, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01901836

A. N. Landsbury, J. M. Thompson, and H. B. Stewart, Basin erosion in the twin-well duffing oscillator : two distinct bifurcation scenarios, International Journal of Bifurcation and Chaos, vol.2, pp.505-532, 1992.

, Nonlinear Dispersive Equations : Local and Global Analysis. CBMS Regional Conference Series in Mathematics, 2006.

Y. P. Wu, J. Cao, D. J. Inman, S. Liu, W. Wang et al., Impact-induced high-energy orbits of nonlinear energy harvesters, Applied Physics Letters, vol.106, p.93901, 2015.

A. Masuda, A. Senda, T. Sanada, and A. Sone, Global stabilization of high-energy response for a duffing-type wideband nonlinear energy harvester via self-excitation, Journal of Intelligent Material Systems and Structures, vol.24, pp.1598-1612, 2013.

J. P. Udani and A. F. Arrieta, Sustaining high-energy orbits of bi-stable energy harvesters by attractor selection, Applied Physics Letters, vol.111, p.213901, 2017.
DOI : 10.1063/1.5000500

D. Mallick, A. Amann, and S. Roy, Surfing the high energy output branch of nonlinear energy harvesters, Physical Review Letters, vol.117, 2016.

M. I. Dykman and M. A. Krivoglaz, Theory of fluctuational transitions between stable states of a nonlinear oscillator, Sov. Phy. JETP, vol.50, pp.30-37, 1979.

R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, Signal amplification in a nanomechanical duffing resonator via stochastic resonance, Applied Physics Letters, vol.90, p.13508, 2007.
DOI : 10.1063/1.2430689

URL : http://arxiv.org/pdf/cond-mat/0611049

A. Badel and E. Lefeuvre, Nonlinear Conditioning Circuits for Piezoelectric Energy Harvesters, Nonlinearity in Energy Harvesting Systems Nonlinear, pp.321-359, 2016.
DOI : 10.1007/978-3-319-20355-3_10

URL : https://hal.archives-ouvertes.fr/hal-02042560

E. Lefeuvre, A. Badel, C. Richard, L. Petit, and D. Guyomar, A comparison between several vibration-powered piezoelectric generators for standalone systems, Sensors and Actuators A : Physical, vol.126, pp.405-416, 2006.
DOI : 10.1016/j.sna.2005.10.043

G. K. Ottman, C. Archin, H. Hofmann, and G. A. Lesieutre, Adaptative piezoelectric energy harvesting circuit for wireless remote power supply, IEEE Transactions on Power Electronics, vol.17, pp.669-676, 2002.
DOI : 10.1109/tpel.2002.802194

G. K. Ottman, H. 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, pp.696-703, 2003.

J. R. Liang and W. H. Liao, Piezoelectric Energy Harvesting and Dissipation on Structural Damping, Journal of Intelligent Material Systems and Structures, vol.20, pp.515-527, 2009.

D. Guyomar, A. Badel, E. Lefeuvre, and C. Richard, Toward Energy Harvesting Using Active Materials and Conversion Improvement by Nonlinear Processing, IEEE transactions on ultrasonics, ferroelectrics, and frequency control, vol.52, pp.584-595, 2005.

E. Lefeuvre, A. Badel, C. Richard, and D. Guyomar, Piezoelectric energy harvesting device optimization by synchronous charge extraction, Journal of Intelligent Material Systems and Structures, vol.16, pp.865-876, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00404199

G. W. Taylor, J. R. Burns, S. M. Kammann, W. B. Powers, and T. R. Welsh, The Energy Harvesting Eel : A Small Subsurface Ocean / River Power Generator, IEEE Journal of Oceanic Engineering, vol.26, pp.539-547, 2001.

L. Garbuio, M. Lallart, D. Guyomar, C. Richard, and D. Audigier, Mechanical Energy Harvester With Ultralow Threshold Rectification Based on SSHI Nonlinear Technique, IEEE Transactions on Industrial Electronics, vol.56, pp.1048-1056, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01699662

E. Lefeuvre, G. Sebald, D. Guyomar, M. Lallart, and C. Richard, Materials , structures and power interfaces for efficient piezoelectric energy harvesting, Journal of Electroceramics, vol.22, pp.171-179, 2009.

M. Lallart, L. Garbuio, L. Petit, C. Richard, and D. Guyomar, Double Synchronized Switch Harvesting (DSSH) : A New Energy Harvesting Scheme for Efficient Energy Extraction, IEEE transactions on ultrasonics, ferroelectrics, and frequency control, vol.55, pp.2119-2130, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01699499

W. Q. Liu, A. Badel, F. Formosa, Y. P. Wu, and A. Agbossou, Wideband energy harvesting using a combination of an optimized synchronous electric charge extraction circuit and a bistable harvester, Smart Materials and Structures, vol.22, p.125038, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01322285

Y. Y. Chen, D. Vasic, and Y. P. Liu, Study of a piezoelectric switching circuit for energy harvesting with bistable broadband technique by work-cycle analysis, Journal of Intelligent Material Systems and Structures, vol.24, pp.180-193, 2013.

L. Alari, J. P. Udani, A. F. Arrieta, and F. Braghin, Synchronized switch technique based on dynamical state of bi-stable energy harvesters, Proceedings of SPIE, vol.10595, pp.1-13, 2018.

C. Buttay, Dspace au LGEF : guide local, 2005.

G. Savelli, P. Coronel, and T. Huguet, Device with deformable shell including an internal piezoelectric circuit, U.S. Patent Application No, vol.15, pp.24-2017
URL : https://hal.archives-ouvertes.fr/hal-02153335

A. Badel, F. Formosa, and T. Huguet, Récupérateur d'énergie vibratoire, numéro de demande FR1870615, 2018.

T. Huguet, A. Badel, and M. Lallart, Exploiting bistable oscillator subharmonics for magnified broadband vibration energy harvesting, Applied Physics Letters, p.173905, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01764325

T. Huguet, A. Badel, O. Druet, and M. Lallart, Drastic bandwidth enhancement of bistable energy harvesters : Study of subharmonic behaviors and their stability robustness, vol.226, pp.607-617, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01901836

?. Huguet, T. Lallart, M. Badel, and A. , Orbit jump in bistable energy harvesters through buckling level modification. Mechanical Systems and Signal Processing, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02092544

?. Huguet, T. Lallart, M. Badel, and A. , Bistable vibration energy harvester and SECE circuit : exploring their mutual influence, Nonlinear Dynamics, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02152838

, Conférences internationales avec actes

T. Huguet, A. Badel, O. Druet, and M. Lallart, Subharmonic orbits and their stability robustness to greatly enhance the bandwidth of bistable vibration energy harvesters, Proceedings of SPIE (mars 2018 à, pp.1-12, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02013598

, Conférences nationales avec actes

T. Huguet, A. Badel, O. Druet, and M. Lallart, Significant enhancement of bistable energy harvesters bandwidth : subharmonic orbits and their stability robustness. JNRSE (mai, 2018.
DOI : 10.1016/j.apenergy.2018.06.011

URL : https://hal.archives-ouvertes.fr/hal-02013626

T. Huguet, A. Badel, and M. Lallart, Exploiting bistable subharmonic orbits for a widen vibration energy harvesting bandwidth, JNRSE, 2017.
DOI : 10.1063/1.5001267

URL : https://hal.archives-ouvertes.fr/hal-02013615

, Journée GDR sans actes

T. Huguet, A. Badel, and M. Lallart, Récupération d'énergie vibratoire non linéaire. GDR SEEDS : "Matériaux actifs et phénomènes couplés, 2017.

T. Huguet, A. Badel, and M. Lallart, Récupération d'énergie vibratoire non linéaire : Exploitation des oscillateurs bistables pour améliorer la bande passante des générateurs, Matériaux actifs et phénomènes couplés, 2017.