Nonlinear vibration analysis of piezoelectric bending actuators: Theoretical and experimental studies

Pouyan Shahabi; Hamed Ghafarirad; Afshin Taghvaeipour

doi:10.1016/j.crme.2019.10.007

Nonlinear vibration analysis of piezoelectric bending actuators: Theoretical and experimental studies

Pouyan Shahabi ¹ ; Hamed Ghafarirad ¹ ; Afshin Taghvaeipour ¹

¹ Mechanical Engineering Department, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

Comptes Rendus. Mécanique, Volume 347 (2019) no. 12, pp. 953-966.

Résumé

Piezoelectric bimorph actuators are used in a variety of applications, including micro positioning, vibration control, and micro robotics. The nature of the aforementioned applications calls for the dynamic characteristics identification of actuator at the embodiment design stage. For decades, many linear models have been presented to describe the dynamic behavior of this type of actuators; however, in many situations, such as resonant actuation, the piezoelectric actuators exhibit a softening nonlinear behavior; hence, an accurate dynamic model is demanded to properly predict the nonlinearity. In this study, first, the nonlinear stress–strain relationship of a piezoelectric material at high frequencies is modified. Then, based on the obtained constitutive equations and Euler–Bernoulli beam theory, a continuous nonlinear dynamic model for a piezoelectric bending actuator is presented. Next, the method of multiple scales is used to solve the discretized nonlinear differential equations. Finally, the results are compared with the ones obtained experimentally and nonlinear parameters are identified considering frequency response and phase response simultaneously. Also, in order to evaluate the accuracy of the proposed model, it is tested out of the identification range as well.

Reçu le : 2019-04-30
Accepté le : 2019-10-31
Publié le : 2019-11-26

DOI : 10.1016/j.crme.2019.10.007

Mots clés : Piezoelectric bending actuator, Euler–Bernoulli beam theory, Nonlinear behavior, Multiple scales

Affiliations des auteurs :

Pouyan Shahabi ¹ ; Hamed Ghafarirad ¹ ; Afshin Taghvaeipour ¹

¹ Mechanical Engineering Department, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

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     author = {Pouyan Shahabi and Hamed Ghafarirad and Afshin Taghvaeipour},
     title = {Nonlinear vibration analysis of piezoelectric bending actuators: {Theoretical} and experimental studies},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {953--966},
     publisher = {Elsevier},
     volume = {347},
     number = {12},
     year = {2019},
     doi = {10.1016/j.crme.2019.10.007},
     language = {en},
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Pouyan Shahabi; Hamed Ghafarirad; Afshin Taghvaeipour. Nonlinear vibration analysis of piezoelectric bending actuators: Theoretical and experimental studies. Comptes Rendus. Mécanique, Volume 347 (2019) no. 12, pp. 953-966. doi : 10.1016/j.crme.2019.10.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.10.007/

Bibliographie
Cité par

[1] N. Hosseini; A.P. Nievergelt; J.D. Adams; V.T. Stavrov; G.E. Fantner A monolithic MEMS position sensor for closed-loop high-speed atomic force microscopy, Nanotechnology, Volume 27 (2016)

[2] J. Lee; W. Choi; Y.K. Yoo; K.S. Hwang; S.M. Lee; S. Kang et al. A micro-fabricated force sensor using an all thin film piezoelectric active sensor, Sensors (Basel), Volume 14 (2014), pp. 22199-22207

[3] G. Yan; H. Ying; Y. Linguo; H. Jisheng; H. Youjin; Y. Yanchun et al. Piezoelectric sensor for micro mass detection, 2016 13th International Computer Conference on Wavelet Active Media Technology and Information Processing (ICCWAMTIP), 2016, pp. 111-113

[4] H. Abdelmoula; S. Zimmerman; A. Abdelkefi Accurate modeling, comparative analysis, and performance enhancement of broadband piezoelectric energy harvesters with single and dual magnetic forces, Int. J. Non-Linear Mech., Volume 95 (2017), pp. 355-363

[5] C. Dagdeviren; P. Joe; O.L. Tuzman; K.-I. Park; K.J. Lee; Y. Shi et al. Recent progress in flexible and stretchable piezoelectric devices for mechanical energy harvesting, sensing and actuation, Extrem. Mech. Lett., Volume 9 (2016), pp. 269-281

[6] H. Ghafarirad; S.M. Rezaei; M. Zareinejad; A.A.D. Sarhan Disturbance rejection-based robust control for micropositioning of piezoelectric actuators, C. R. Mecanique, Volume 342 (2014), pp. 32-45

[7] R.K. Jain; S. Majumder; B. Ghosh; S. Saha Design and manufacturing of mobile micro manipulation system with a compliant piezoelectric actuator based micro gripper, J. Manuf. Syst., Volume 35 (2015), pp. 76-91

[8] H.-K. Ma; W.-F. Luo; J.-Y. Lin Development of a piezoelectric micropump with novel separable design for medical applications, Sens. Actuators A, Phys., Volume 236 (2015), pp. 57-66

[9] X. Chen; Z. Chen; X. Li; L. Shan; W. Sun; X. Wang et al. A spiral motion piezoelectric micromotor for autofocus and auto zoom in a medical endoscope, Appl. Phys. Lett., Volume 108 (2016)

[10] M. Rakotondrabe; I.A. Ivan; S. Khadraoui; P. Lutz; N. Chaillet Simultaneous displacement/force self-sensing in piezoelectric actuators and applications to robust control, IEEE/ASME Trans. Mechatron., Volume 20 (2015), pp. 519-531

[11] A. Mystkowski; A.P. Koszewnik Mu-Synthesis robust control of 3D bar structure vibration using piezo-stack actuators, Mech. Syst. Signal Process., Volume 78 (2016), pp. 18-27

[12] D. Mazeika; P. Vasiljev; S. Borodinas; R. Bareikis; Y. Yang Small size piezoelectric impact drive actuator with rectangular bimorphs, Sens. Actuators A, Phys., Volume 280 (2018), pp. 76-84

[13] A. Erturk; D.J. Inman An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations, Smart Mater. Struct., Volume 18 (2009)

[14] A. Erturk; D.J. Inman A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters, J. Vib. Acoust., Volume 130 (2008)

[15] H. Ghafarirad; S.M. Rezaei; A.A.D. Sarhan; M. Zareinejad Continuous dynamic modelling of bimorph piezoelectric cantilevered actuators considering hysteresis effect and dynamic behaviour analysis, Math. Comput. Model. Dyn. Syst., Volume 21 (2015) no. 2, pp. 130-152 | DOI

[16] R. Hosseini; M. Hamedi; A. Ebrahimi Mamaghani; H.C. Kim; J. Kim; J. Dayou Parameter identification of partially covered piezoelectric cantilever power scavenger based on the coupled distributed parameter solution, Int. J. Smart Nano Mater., Volume 8 (2017), pp. 110-124

[17] S.S. Raju; M. Umapathy; G. Uma High-output piezoelectric energy harvester using tapered beam with cavity, J. Intell. Mater. Syst. Struct., Volume 29 (2018), pp. 800-815

[18] H. Ghafarirad; S.M. Rezaei; M. Zareinejad; M. Hamdi; R.J. Ansari Robust control with unknown dynamic estimation for multi-axial piezoelectric actuators with coupled dynamics, C. R. Mecanique, Volume 340 (2012), pp. 646-660

[19] P.P. Chao; P.-Y. Liao; M.-Y. Tsai; C.-T. Lin Robust control design for precision positioning of a generic piezoelectric system with consideration of microscopic hysteresis effects, Microsyst. Technol., Volume 17 (2011), pp. 1009-1023

[20] S.C. Stanton; A. Erturk; B.P. Mann; D.J. Inman Nonlinear piezoelectricity in electroelastic energy harvesters: modeling and experimental identification, J. Appl. Phys., Volume 108 (2010)

[21] S.C. Stanton; A. Erturk; B.P. Mann; E.H. Dowell; D.J. Inman Nonlinear nonconservative behavior and modeling of piezoelectric energy harvesters including proof mass effects, J. Intell. Mater. Syst. Struct., Volume 23 (2012), pp. 183-199

[22] S. Leadenham; A. Erturk Nonlinear M-shaped broadband piezoelectric energy harvester for very low base accelerations: primary and secondary resonances, Smart Mater. Struct., Volume 24 (2015)

[23] D. Tan; P. Yavarow; A. Erturk Nonlinear elastodynamics of piezoelectric macro-fiber composites with interdigitated electrodes for resonant actuation, Compos. Struct., Volume 187 (2018), pp. 137-143

[24] R.G. Ballas Piezoelectric Multilayer Beam Bending Actuators Static and Dynamic Behavior and Aspects of Sensor Integration, Springer, New York, 2007

[25] A. Chattopadhyay; C.E. Seeley A higher order theory for modeling composite laminates with induced strain actuators, Composites, Part B, Eng., Volume 28 (1997), pp. 243-252

[26] A. Abdelkefi; A.H. Nayfeh; M.R. Hajj Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation, Nonlinear Dyn., Volume 67 (2012), pp. 1221-1232

[27] A. Abdelkefi; A.H. Nayfeh; M.R. Hajj Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters, Nonlinear Dyn., Volume 67 (2012), pp. 1147-1160

[28] K. Mam; M. Peigney; D. Siegert Finite strain effects in piezoelectric energy harvesters under direct and parametric excitations, J. Sound Vib., Volume 389 (2017), pp. 411-437

[29] V. Guillot; A.T. Savadkoohi; C.-H. Lamarque Analysis of a reduced-order nonlinear model of a multi-physics beam, Nonlinear Dyn., Volume 97 (2019) no. 2, pp. 1371-1401

[30] S.C. Stanton; A. Erturk; B.P. Mann; D.J. Inman Resonant manifestation of intrinsic nonlinearity within electroelastic micropower generators, Appl. Phys. Lett., Volume 97 (2010)

[31] A.H. Nayfeh; D.T. Mook Nonlinear Oscillations, John Wiley & Sons, 2008

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