, La fréquence des vibrations, l?amplitude de déplacement du pot-vibrant pour une fréquence donnée, soit son accélération

. Bibliographie,

R. Seveno and D. Averty, « Ultra light tunable capacitor based on PZT thin film deposited onto aluminium foil », Journal of Sol-Gel Science and Technology, vol.68, issue.2, pp.175-179, 2013.

S. Roundy, P. K. Wright, and J. Rabaey, « A study of low level vibrations as a power source for wireless sensor nodes, Computer Communications, vol.26, issue.11, pp.1131-1144, 2003.

S. Beeby and N. White, Energy harvesting for autonomous systems, 2010.

S. J. Roundy, « Energy scavenging for wireless sensor nodes with a focus on vibration to electricity conversion, 2003.

S. P. Beeby, « A micro electromagnetic generator for vibration energy harvesting, Journal of Micromechanics and Microengineering, vol.17, issue.7, pp.1257-1265, 2007.

S. Kim, H. Park, S. Kim, H. C. Wikle, J. Park et al., « Comparison of MEMS PZT Cantilevers Based on $d_{31}$ and $d_{33}$ Modes for Vibration Energy Harvesting, Journal of Microelectromechanical Systems, vol.22, issue.1, pp.26-33, 2013.

C. B. Williams and R. B. Yates, Analysis of a micro-electric generator for microsystems, Sensors and Actuators A: Physical, vol.52, issue.1, pp.8-11, 1996.

C. Shearwood and R. B. Yates, « Development of an electromagnetic microgenerator, Electronics Letters, vol.33, pp.1883-1884, 1997.

J. C. Park, D. H. Bang, J. Y. Park, and . Micro, Fabricated Electromagnetic Power Generator to Scavenge Low Ambient Vibration, IEEE Transactions on Magnetics, vol.46, issue.6, pp.1937-1942, 2010.

D. Hoffmann, C. Kallenbach, M. Dobmaier, B. Folkmer, and Y. Manoli, Flexible polyimide film technology for vibration energy harvesting, Proceedings of PowerMEMS, pp.344-347, 2009.

Y. Choi, « Low Frequency Vibration Energy Harvester Using Spherical Permanent Magnet with Non-uniform Mass Distribution, J. Phys.: Conf. Ser, vol.476, issue.1, p.12123, 2013.

S. D. Moss, G. A. Hart, S. K. Burke, and G. P. Carman, « Hybrid rotary-translational vibration energy harvester using cycloidal motion as a mechanical amplifier, Appl. Phys. Lett, vol.104, issue.3, p.33506, 2014.

M. El-hami, « Design and fabrication of a new vibration-based electromechanical power generator, Sensors and Actuators A: Physical, vol.92, pp.335-342, 2001.

E. P. James, « An investigation of self-powered systems for condition monitoring applications, Sensors and Actuators A: Physical, vol.110, pp.171-176, 2004.

L. Bian, Y. Wen, P. Li, Q. Gao, and M. Zheng, « Magnetoelectric transducer with high quality factor for wireless power receiving, Sensors and Actuators A: Physical, vol.150, issue.2, pp.207-211, 2009.

J. Yang, Y. Wen, P. Li, X. Yue, Q. Yu et al., « A two-dimensional broadband vibration energy harvester using magnetoelectric transducer, Applied Physics Letters, vol.103, p.243903, 2013.

L. Zhang, S. W. Or, and C. M. Leung, « Voltage-mode direct-current magnetoelectric sensor based on piezoelectric-magnetostrictive heterostructure, Journal of Applied Physics, vol.117, pp.17-748, 2015.

S. Roundy, P. K. Wright, and K. S. Pister, « Micro-electrostatic vibration-to-electricity converters, ASME 2002 International Mechanical Engineering Congress and Exposition, pp.487-496, 2002.

C. Sun, J. Shi, D. J. Bayerl, and E. X. Wang, PVDF microbelts for harvesting energy from respiration, vol.4, p.4508, 2011.

D. Chen, T. Sharma, and J. X. Zhang, « Mesoporous surface control of PVDF thin films for enhanced piezoelectric energy generation, Sensors and Actuators A: Physical, vol.216, pp.196-201, 2014.

G. Suchaneck, « Deposition of PZT thin film onto copper-coated polymer films by mean of pulsed-DC and RF-reactive sputtering, Surface and Coatings Technology, vol.205, pp.241-244, 2011.

S. Y. Chung, « All-Solution-Processed Flexible Thin Film Piezoelectric Nanogenerator, Adv. Mater, vol.24, pp.6022-6027, 2012.

J. H. Rho, J. H. Ahn, N. Lee, and J. Ahn, Mechanically flexible PZT thin films on plastic substrates, pp.246-247, 2010.

Y. H. Do, M. G. Kang, J. S. Kim, C. Y. Kang, and S. J. Yoon, « Fabrication of flexible device based on PAN-PZT thin films by laser lift-off process, Sensors and Actuators A: Physical, vol.184, pp.124-127, 2012.

Y. H. Do, W. S. Jung, M. G. Kang, C. Y. Kang, and S. J. Yoon, « Preparation on transparent flexible piezoelectric energy harvester based on PZT films by laser lift-off process, Sensors and Actuators A: Physical, vol.200, pp.51-55, 2013.

H. Liu, C. J. Tay, C. Quan, T. Kobayashi, and C. Lee, « Piezoelectric MEMS Energy Harvester for Low-Frequency Vibrations With Wideband Operation Range and Steadily Increased Output Power, Journal of Microelectromechanical Systems, vol.20, issue.5, pp.1131-1142, 2011.

Y. J. Ko, « Flexible Pb(Zr0.52Ti0.48)O3 Films for a Hybrid PiezoelectricPyroelectric Nanogenerator under Harsh Environments, ACS Appl. Mater. Interfaces, vol.8, issue.10, pp.6504-6511, 2016.

Y. Zhou, D. J. Apo, and E. S. Priya, « Dual-phase self-biased magnetoelectric energy harvester, Applied Physics Letters, vol.103, 2013.

Y. Zhou, S. Yang, D. J. Apo, D. Maurya, and E. S. Priya, « Tunable self-biased magnetoelectric response in homogenous laminates, Applied Physics Letters, vol.101, issue.23, p.232905

K. Park, Highly-Efficient, Flexible Piezoelectric PZT Thin Film Nanogenerator on Plastic Substrates, vol.26, pp.2514-2520, 2014.

C. K. Jeong, « Flexible highly-effective energy harvester via crystallographic and computational control of nanointerfacial morphotropic piezoelectric thin film, Nano Research, vol.10, issue.2, pp.437-455, 2017.

G. Lippmann, . Annales-de-chimie, and . De-physique, Annales de chimie et de physique, vol.24, pp.145-177, 1881.

P. Curie and J. Curie, Contractions et dilatations produites par des tensions électriques dans les cristaux hémièdres à faces inclinées », Comptes rendus de l'Académie des sciences, vol.XCIII, p.1137

M. Cueff and . Micro, , 2011.

«. Ieee, , pp.0-1, 1988.

P. Muralt, A. Kholkin, M. Kohli, and E. T. Maeder, « Piezoelectric actuation of PZT thinfilm diaphragms at static and resonant conditions, Sensors and Actuators A: Physical, vol.53, pp.398-404, 1996.

, « PZT phase diagram.jpg (Image JPEG, 617 × 471 pixels)

. Disponible,

D. Pandey, A. K. Singh, and E. S. Baik, « Stability of ferroic phases in the highly piezoelectric Pb(Zr x Ti 1?x )O 3 ceramics, Acta Crystallographica Section A Foundations of Crystallography, vol.64, issue.1, pp.192-203, 2008.

«. Photolithographie,

. Disponible,

«. Gateway, Tutorial on wet coating technologies

L. N. Chapin and S. A. Myers, « Microstructure Characterization of Ferroelectric Thin Films used in Non-Volatile Memories-Optical and Scanning Electron Microscopy, Symposium Y-Ferroelectric Thin Films I, vol.200, 1990.

A. Iembo, « Preparation of Pb(Ti,Zr)O3/RuO2 multilayers in situ by pulsed laser ablation deposition, Integrated Ferroelectrics, vol.18, pp.397-404, 1997.

B. A. Tuttle, R. W. Schwartz, D. H. Doughty, J. Voigt, and A. H. Carim, Characterization of Chemically Prepared PZT Thin Films », in Symposium YFerroelectric Thin Films I, vol.200, 1990.

J. H. Yi, R. Seveno, and H. W. Gundel, Sol-gel derived PZT/RuO2 multilayer films on stainless steel substrates », Integrated Ferroelectrics, vol.23, pp.199-214, 1999.

J. Joo, D. Kill, and S. Joo, Effect of Pb Content on the Transformation of Sputtered PbxZr0.4Ti0.6O3 Thin Film », in Symposium E-Crystallization and Related Phenomena in Amorphous Materials-Ceramics, Metals, Polymers, and Semiconductors, vol.321, 1993.

K. G. Brooks, I. M. Reaney, R. Klissurska, Y. Huang, L. Bursill et al., « Orientation of rapid thermally annealed lead zirconate titanate thin films on (111) Pt substrates », Journal of Materials Research, vol.9, issue.10, pp.2540-2553, 1994.

O. Babushkin, T. Lindbäck, K. Brooks, and N. Setter, « PZT phase formation monitored by high-temperature X-ray diffractometry », Journal of the European Ceramic Society, vol.17, issue.6, pp.813-818, 1997.

G. W. Scherer, Aging and drying of gels », Journal of Non-Crystalline Solids, vol.100, issue.1-3, pp.77-92, 1988.

J. F. Scott, L. D. Mcmillan, and C. A. Araujo, « Switching kinetics of lead zirconate titanate sub-micron thin-film memories, Ferroelectrics, vol.93, issue.1, pp.31-36, 1989.

, André Perrin de l'Université de Rennes 1)

«. and W. , , pp.19-2017

A. Hammiche, L. Bozec, H. M. Pollock, M. German, and M. Reading, « Progress in nearfield photothermal infra-red microspectroscopy, Journal of Microscopy, vol.213, issue.2, pp.129-134, 2004.

«. Doitpoms and -. Tlp, Library Ferroelectric Materials-Measurement of polarisation

. Disponible,

F. Xu and F. Chu, Trolier-McKinstry, « Longitudinal piezoelectric coefficient measurement for bulk ceramics and thin films using pneumatic pressure rig, Journal of Applied Physics, vol.86, issue.1, p.588, 1999.

N. Ledermann, « {1 0 0}-Textured, piezoelectric Pb(Zrx, Ti1?x)O3 thin films for MEMS: integration, deposition and properties, Sensors and Actuators A: Physical, vol.105, issue.2, pp.162-170, 2003.

A. L. Kholkin, C. Wütchrich, D. V. Taylor, and E. N. Setter, « Interferometric measurements of electric field-induced displacements in piezoelectric thin films, Review of Scientific Instruments, vol.67, issue.5, p.1935, 1996.

H. Jacobsen, K. Prume, B. Wagner, K. Ortner, and E. T. Jung, High-rate sputtering of thick PZT thin films for MEMS, J Electroceram, vol.25, issue.2-4, pp.198-202, 2010.

I. Kanno, H. Kotera, and E. K. Wasa, « Measurement of transverse piezoelectric properties of PZT thin films, Sensors and Actuators A: Physical, vol.107, issue.1, pp.68-74, 2003.

K. Sivanandan, A. T. Achuthan, V. Kumar, and E. I. Kanno, « Fabrication and transverse piezoelectric characteristics of PZT thick-film actuators on alumina substrates, Sensors and Actuators A: Physical, vol.148, issue.1, pp.134-137, 2008.

C. H. Nguyen and S. J. Pietrzko, « Piezoelectric-mechanical-acoustic couplings from a PZT-actuated vibrating beam and its sound radiation, Mechanical Systems and Signal Processing, vol.18, pp.929-945, 2004.

F. K. Kneubühl, Oscillations and waves, 1997.

J. G. Smits and W. Choi, « The constituent equations of piezoelectric heterogeneous bimorphs, Ultrasonics, Ferroelectrics and Frequency Control, vol.38, issue.3, pp.256-270, 1991.

J. G. Gardeniers, A. G. Verholen, N. R. Tas, and M. C. Elwenspoek, « Direct measurement of piezoelectric properties of Sol-Gel PZT films », Journal of the Korean Physical Society, vol.32, pp.1573-1577, 1998.

E. Boucher, B. Guiffard, L. Lebrun, and E. D. Guyomar, )-doped lead zirconate titanate ceramics, Effects of Zr/Ti ratio on structural, dielectric and piezoelectric properties of Mn-and, vol.32, pp.479-485, 2006.

O. Auciello, K. D. Gifford, and A. I. Kingon, « Control of structure and electrical properties of lead-zirconium-titanate-based ferroelectric capacitors produced using a layer-by-layer ion beam sputter-deposition technique, Applied Physics Letters, vol.64, pp.2873-2875, 1994.

D. P. Vijay, C. K. Kwok, W. Pan, I. K. Yoo, and S. B. Desu, « Electrode effects on electrical properties of ferroelectric thin films, Proceedings of the Eighth IEEE International Symposium on Applications of Ferroelectrics, 1992. ISAF '92, pp.408-411, 1992.

G. Yi and M. Sayer, « Sol-gel processing of complex oxide films, American Ceramic Society bulletin, vol.70, issue.7, pp.1173-1179, 1991.

R. Seveno, P. Limousin, D. Averty, J. Chartier, R. Le-bihan et al., « Preparation of multi-coating PZT thick films by sol-gel method onto stainless steel substrates, Journal of the European Ceramic Society, vol.20, pp.2025-2028, 2000.

C. K. Kwok and S. B. Desu, « Pyrochlore to perovskite phase transformation in sol-gel derived lead-zirconate-titanate thin films, Applied Physics Letters, vol.60, pp.1430-1432, 1992.

K. R. Udayakumar, P. J. Schuele, J. Chen, S. B. Krupanidhi, and L. E. Cross, « Thicknessdependent electrical characteristics of lead zirconate titanate thin films, Journal of Applied Physics, vol.77, issue.8, pp.3981-3986, 1995.

L. Lian and N. R. Sottos, « Effects of thickness on the piezoelectric and dielectric properties of lead zirconate titanate thin films », Journal of Applied Physics, vol.87, issue.8, pp.3941-3949, 2000.

K. R. Bellur, H. N. Al-shareef, S. H. Rou, K. D. Gifford, O. Auciello et al., « Electrical characterization of sol-gel derived PZT thin films, Proceedings of the Eighth IEEE International Symposium on Applications of Ferroelectrics, 1992. ISAF '92, pp.448-451, 1992.

M. Sitti, « PZT actuated four-bar mechanism with two flexible links for micromechanical flying insect thorax, ICRA. IEEE International Conference on, vol.4, pp.3893-3900, 2001.

T. Harigai, H. Adachi, and E. E. Fujii, « Vibration energy harvesting using highly (001)oriented Pb(Zr,Ti)O[sub 3] thin film, Journal of Applied Physics, vol.107, issue.9, p.96101, 2010.
DOI : 10.1063/1.3406253

K. Morimoto, I. Kanno, K. Wasa, and H. Kotera, « High-efficiency piezoelectric energy harvesters of c-axis-oriented epitaxial PZT films transferred onto stainless steel cantilevers, Sensors and Actuators A: Physical, vol.163, issue.1, pp.428-432, 2010.
DOI : 10.1016/j.sna.2010.06.028

D. Chun, M. Sato, and E. I. Kanno, « Precise measurement of the transverse piezoelectric coefficient for thin films on anisotropic substrate, Journal of Applied Physics, vol.113, p.44111, 2013.

I. Kanno, « High efficiency energy harvester of transferred epitaxial PZT films on stainless steel sheets, Micro Electro Mechanical Systems (MEMS), pp.152-155, 2010.

Y. Li, J. Sun, C. Yang, J. Liu, S. Sugiyama et al., « Fabrication and Characterization of a Lead Zirconate Titanate Micro Energy Harvester Based on Eutectic Bonding, Chinese Physics Letters, vol.28, issue.6, p.68103, 2011.

A. J. Dick, « Characterizing Effective d31 Values for PZT from the Nonlinear Oscillations of Clamped-Clamped Micro-Resonators », Strojni?ki vestnik, Journal of Mechanical Engineering, vol.59, pp.50-55, 2013.

M. Dekkers, « The significance of the piezoelectric coefficient d 31,eff determined from cantilever structures, Journal of Micromechanics and Microengineering, vol.23, issue.2, p.25008, 2013.

T. Kobayashi, Y. Suzuki, N. Makimoto, H. Funakubo, and E. R. Maeda, Activation of piezoelectric property of PZT thin films by pulse poling », Journal of Physics: Conference Series, vol.557, p.12130, 2014.

H. Liu, S. Zhang, T. Kobayashi, T. Chen, and C. Lee, « Flow sensing and energy harvesting characteristics of a wind-driven piezoelectric Pb (Zr0. 52, Ti0. 48) O 3 microcantilever, Micro & Nano Letters, vol.9, issue.4, pp.286-289, 2014.

C. K. Jeong, « Self-powered fully-flexible light-emitting system enabled by flexible energy harvester, Energy Environ. Sci, vol.7, pp.4035-4043, 2014.

N. Chidambaram, A. Mazzalai, and P. Muralt, « Measurement of effective piezoelectric coefficients of PZT thin films for energy harvesting application with interdigitated electrodes, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.59, issue.8, pp.1624-1631

J. P. Mercier, G. Zambelli, and E. W. Kurz, Introduction à la science des matériaux, 1999.

S. Baron, « Polymère souple pour antenne patch électriquement accordable en bande X : conception et caractérisations », Theses, 2015.

M. Roussel, « Electromechanical study of polyurethane films with carbon black nanoparticles for MEMS actuators, J. Micromech. Microeng, vol.24, issue.5, p.55011, 2014.

, « Polyéthylène téréphthalate-catalogue en-ligne-fournisseur de materiaux en petites quantites pour la recherche-Goodfellow

S. Kim, H. Park, S. Kim, H. C. Wikle, J. Park et al., « Comparison of MEMS PZT Cantilevers Based on $d_{31}$ and $d_{33}$ Modes for Vibration Energy Harvesting, Journal of Microelectromechanical Systems, vol.22, issue.1, pp.26-33, 2013.

C. Blanchard, « Comportement d'un récupérateur d'énergie constitué d'une lame piézoélectrique souple : approche analytique, numérique et expérimentale », Stage M2, 2016.

E. Boucher, Elaboration et caractérisation de céramiques PZT bi-substituees et modélisation non-linéaire de leur comportement en contrainte et en champ électrique, 2002.

M. Budinger, « Contribution à la conception et à la modélisation d'actionneurs piézoélectriques cylindriques à deux degrés de liberté de type rotation et translation, 2003.

E. M. Bourim, « Contribution à l'étude par spectrométrie mécanique du comportement anélastique de céramiques piézoélectriques de type Pb (Zr 1-x Ti x) O3 », 1998.

G. Sebald, « Nouveaux monocristaux à forte conversion piézoélectrique: croissance, modélisation et caractérisation », Institut national des sciences appliquées de Lyon, 2004.

A. Albareda, P. Gonnard, V. Perrin, R. Briot, and E. D. Guyomar, « Characterization of the mechanical nonlinear behavior of piezoelectric ceramics, IEEE transactions on ultrasonics, ferroelectrics, and frequency control, vol.47, issue.4, pp.844-853, 2000.

J. F. Shepard and P. J. Moses, Trolier-McKinstry, « The wafer flexure technique for the determination of the transverse piezoelectric coefficient (d31) of PZT thin films, Sensors and Actuators A: Physical, vol.71, issue.2, pp.133-138, 1998.

P. , « Piezoelectric cantilever beams actuated by PZT sol-gel thin film, Sensors and Actuators A: Physical, vol.54, pp.530-535, 1996.

Y. B. Jeon, R. Sood, J. Jeong, and S. Kim, « MEMS power generator with transverse mode thin film PZT, Sensors and Actuators A: Physical, vol.122, issue.1, pp.16-22, 2005.

F. Casset, « Young modulus and Poisson ratio of PZT thin film by Picosecond Ultrasonics, Ultrasonics Symposium (IUS), pp.2180-2183, 2012.

J. Ducarne, « Modélisation et optimisation de dispositifs non-linéaires d'amortissement de structures par systèmes piézoélectriques commutés, 2009.

M. Defosseux, Conception et caractérisation de microgénérateurs piézoélectriques pour microsystèmes autonomes, 2011.

P. Bechterew, « Analytical study of the generalized Hooke's law. Application of the method of coordinate transformation, Zh. Russ. Fiz.-Khim. Obshch. Leningrad. Univ., Fizika, vol.58, issue.3, pp.415-416, 1926.

L. Gornet, Généralités sur les matériaux composites, 2008.

M. Brissaud, Matériaux piézoélectriques: caractérisation, modélisation et vibration. PPUR presses polytechniques, 2007.

P. Pichon and F. Chemin, « Étude d'une lame piézoélectrique soumise à un écoulement de fluide, Projet numérique M1, 2017.

I. Aydin, « Comportement d'un brin piézoélectrique dans un milieu appauvri en air, 2017.

Q. Wang, Q. Zhang, B. Xu, R. Liu, and L. E. Cross, « Nonlinear piezoelectric behavior of ceramic bending mode actuators under strong electric fields, Journal of Applied Physics, vol.86, issue.6, p.3352, 1999.

D. J. Li, Polymer piezoelectric energy harvesters for low wind speed, Appl. Phys. Lett, vol.104, issue.1, p.12902, 2014.

A. Badel, « Récupération d'énergie et contrôle vibratoire par éléments piézoélectriques suivant une approche non linéaire », phdthesis, 2005.

P. Jeau, Production d'énergie renouvelable à partir de couches minces piézoélectriques », Stage M1, 2015.

G. Han, )O 3 thick films by thermal expansion mismatch between substrate and Pb(Zr 0.52 Ti 0.48 )O 3 film », Stress-controlled Pb, vol.110, p.124101, 2011.

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, issue.4, pp.584-595, 2005.