Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-17T02:17:14.332Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimisation structurale de problèmes d'amortissement de type shunt résistif

Published online by Cambridge University Press:  23 July 2009

Yann Meyer  and
Manuel Collet
Yann Meyer
Affiliation:
Institut Supérieur de Mécanique de Paris (SupMéca Paris), LISMMA/Structure, 3 rue Fernand Hainaut, 93407 Saint-Ouen Cedex, France
Manuel Collet
Affiliation:
Institut FEMTO ST dép. MA/UMR 6174, 24 chemin de l'épitaphe, 25000 Besançon, France
Get access

Abstract

Les besoins accrus d'encapsulation et d'autonomie des dispositifs de contrôle vibratoire ont ouvert le domaine des matériaux piézoélectriques shuntés. De par ses propriétés physiques, l'élément piézoélectrique convertit une partie d'énergie vibratoire en énergie électrique. Le fait de connecter un circuit électrique (un circuit de shunt) aux bornes du patch modifie la dynamique du système complet (structure + patchs piézoélectriques) et offre ainsi des possibilités de le contrôler. C'est ce que nous nommerons contrôle vibratoire passif dans le cas où le circuit de shunt est constitué de composants passifs (Résistances et inductances physiques). Dans la littérature, les dispositifs employant des stratégies de contrôle se focalisent principalement sur l'efficacité obtenue en termes de facteur d'amortissement modal. Les flux d'énergie entre les différents éléments du système complet ne sont pas optimisés. Nous proposons de développer un critère d'optimisation structurale qui prend en compte la dissipation induite non seulement en termes d'amortissement modal mais également en termes d'amplitude d'énergie dissipée. Ce critère intègre des grandeurs facilement calculables via un code de calcul par éléments-finis. Il est à noter que l'une des principales difficultés de modélisation de ce type de structures est liée à la condition électrique qui varie. Il est nécessaire d'employer un modèle complet ou suffisamment représentatif pour calculer les modes de résonance de la structure à tension nulle (condition de Dirichlet électrique ) et à courant nul (condition de Neumann électrique). Nous appliquerons notre critère à une poutre élancée sur laquelle est implantée un patch piézoélectrique pour différentes conditions aux limites et différents types de polarisation. Nous nous focaliserons sur le contrôle du premier mode de flexion de la structure.

Keywords

Structural optimisationvibration controlpassive dampingresistive shuntpiezoelectricityOptimisation structuralecontrôle vibratoireamortissement passifshunt résistifpiézoélectricité
Type
Research Article
Information
Mechanics & Industry , Volume 10 , Issue 2 , March 2009 , pp. 109 - 120
Copyright
© AFM, EDP Sciences, 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Lin, M., Chang, F.-K., The manufacture of composite structures with a built-in network of piezoceramics, Compos. Sci. Tech. 62 (2002) 919–939 CrossRef
W.J. Staszewski, C. Boller, G.R. Tomlinson, Health Monitoring of Aerospace Structures: Smart Sensor Technologies and Signal Processing, Wiley and New York, 2004
Su, Z., Wang, X., Chen, W., Ye, L., Wang, D., A built-in active sensor network for health monitoring of composite structures, Smart Mater. Struct. 15 (2006) 1939–1949 CrossRef
Scire, F.E., Teague, C.E., Piezodriven 50 $\mu$m range stage with nanometer resolution, Rev. Sci. Instrum. 49 (1978) 1735–1739 CrossRef
S.T. Sith, D.G. Chetwynd, Foundations of ultraprecision mechanism design, Gordon and Breach Science Publishers, 1978
A.H. Slocum, Precision machine design, Prentice-Hall, Inc., 1992
Karnopp, D.C., Trikha, A.K., Comparative study of optimization techniques for shock and vibration isolation, J. Eng. Ind. Trans. ASME 91 (1969) 1128–1132 CrossRef
Kaplow, C.E., Velman, J.R., Active local vibration isolation applied to a flexible space telescope, J. Guid. Contr. Dynam. 3 (1980) 227–233 CrossRef
R.M. Chalasani, Ride performance potential of active suspension systems, Part 1: Simplified analysis based on a quarter-car model, ASME Symposium on simulation and control of ground vehicles and transportation systems, Anaheim, CA, Dec. 1984
C.R. Fuller, S.J. Elliott, P.A. Nelson, Active Control of Vibration, Academic Press, 1996
Meyer, Y., Verdot, T., Collet, M., Baborowski, J., Muralt, P., Active Isolation of Electronic Micro Components with Piezoelectrically-Transduced Silicon MEMS Devices, Smart Mater. Struct. 16 (2007) 128–134 CrossRef
Meyer, Y., Collet, M., Mixed control for robust vibration isolation: numerical energy comparison for an active micro suspension device, Smart Mater. Struct. 16 (2007) 1361–1369 CrossRef
L. Meirovitch, Dynamics and control of structures, New-york and Wiley, 1990
A. Preumont, Vibration Control of Active Structures: An Introduction, Kluwer Academic Publishers, Dordrecht/Boston/London, 2002
Balas, M.J., Direct velocity feedback control of large space structures, J. Guid. Contr. Dynam. 2 (1979) 252–253 CrossRef
Collet, M., Walter, V., Delobelle, P., Active Damping of a Micro-Cantilever Piezo-Composite Beam, J. Sound Vib. 260 (2003) 453–476 CrossRef
Lions, J.L., Exact controllability, stabilization and perturbations for distributed systems, SIAM Rev. 30 (1988) 1–68 CrossRef
Crawley, E.F., de Luis, J., Use piezoelectric actuators as element of intelligent structures, AIAA J. 25 (1987) 1373–1385 CrossRef
Baz, A., Poh, S., Performance of an active control system with piezoelectric actuators, J. Sound Vib. 126 (1988) 327–342 CrossRef
Takagi, T., Sugeno, M., Fuzzy identification of systems and its applications, IEEE SMC 15 (1985) 116–1322
R.E. Bellman, I.L. Glicksberg, O. Gross, On the bang-bang control problem, Rand. Corporation, 1955
Hagood, N.W., Crawley, E.F., Damping of structural vibrations with piezoelectric materials and passive electrical networks, J. Sound Vib. 142 (1991) 243–268 CrossRef
Davis, C.L., Lesieutre, G.A., An actively tuned solid-state vibration absorber using capacitive shunting of piezoelectric stiffness, J. Sound Vib. 232 (2000) 601–617 CrossRef
Forward, R.L., Electromechanical transducer-coupled mechanical structure with negative capacitance compensation circuit, US Patent Specification 4 (1979) 158–787
Behrens, S., Fleming, A.J., Moheimani, S.O.R., A broaband controller for shunt piezoelectric damping of structural vibration, Smart Mater. Struct. 12 (1999) 1–22
S.Y. Wu, Piezoelectric shunts with parallel R-L circuit for smart structural damping and vibration control, In Proc. SPIE Symposium on Smart Structures and Materials – Passive Damping and Isolation, 1996, pp. 259–269
J.J. Hollkamp, Mutlimodal passive vibration suppression with piezoelectric materials and resonant shunt, J. Intell. Mater. Syst. Struct. 5 (1994)
S.Y. Wu, Method for multiple mode shunt damping of structural vibration using a single PZT transducer, In Proc. SPIE Symposium on Smart Structures and Materials – Smart Structures and Intelligent Systems (1998) 159–167
Clark, W.W., Vibration control with state-switching piezoelectric materials, J. Intell. Mater. Syst. Struct. 11 (2000) 263–71 CrossRef
Corr, L.R., Clark, W.W., A novel semi-active multi-modal vibration control law for a piezoceramic actuator, VAJ 125 (2003) 214–222
C. Richard, Enhanced semi passive damping using continuous switching of a piezoelectric device on an inductor, In Proc. SPIE Symposium on Smart Structures and Materials – Passive Damping and Isolation, 2000, pp. 288–299
L. Petit, E. Lefeuvre, C. Richard, D. Guyomar, Broadband semi passive piezoelectric technique for structural damping, In Proc. SPIE Symposium on Smart Structures and Materials – Passive Damping and Isolation, 2004, pp. 414–425
E. Lefeuvre, D. Guyomar, L. Petit, C. Richard, A. Badel, Semi passive structural damping by synchronized switching on voltage sources, SMEBA 03, Suzhou, China, May 2004
Tawfik, M., Baz, A., Experimental and spectral finite element study of plates with shunted piezoelectric patches, Int. J. Acoust. Vib. 9 (2004) 87–97
Takigami, T., Tomioka, T., Investigation to suppress bending vibration of railway vehicle carbodies using piezoelectric elements, QR of RTRI 46 (2005) 225–230 CrossRef
Neubauer, M., Oleskiewcz, R., Suppression of brake squeal using shunted piezoceramics, J. Vib. Acoust. 130 (2008) 021005 CrossRef
Belloli, A., Ermanni, P., Optimum placement of piezoelectric ceramic modules for vibration suppression of highly constrained structures, Smart Mater. Struct. 16 (2007) 1662–1671 CrossRef
Frecker, M.I., Recent advances in optimization of smart structures and actuators, J. Intell. Mater. Syst. Struct. 14 (2003) 207–216 CrossRef
Devasia, S., Meressi, T., Paden, B., Bayo, E., Piezoelectric actuator design for vibration suppression: placement and sizing, J. Guid. Contr. Dynam. 16 (1993) 859–864 CrossRef
H. Kwakernaak, R. Sivan, Linear optimal control systems, Wiley-Interscience, 1972
Dhingra, A.K., Lee, B.H., Optimal placement of actuators in actively controlled structures, Eng. Optim. 23 (1994) 99–118 CrossRef
Arbel, A., Controllability measures and actuator placement in oscillatory systems, Int. J. Contr. 33 (1981) 565–574 CrossRef
Hac, A., Liu, L., Sensor and actuator location in motion control of flexible structures, J. Sound Vib. 167 (1993) 239–261
Dhingra, A.K., Lee, B.H., Multiobjective design of actively controlled structures using a hybrid optimization method, Int. Jour. Num. Meth. Eng. 38 (1995) 3380–3401
Kondoh, S., Yatomi, C., Inoue, K., The positioning of sensors and actuators in the vibration control of flexible systems, JSME 33 (1992) 145–152
Kim, S.J., Jones, J.D., Influence of piezo-actuator thickness on the active vibration control of a cantilever beam, J. Intell. Mater. Syst. Struct. 6 (1995) 610–623
Meric, R.A., Saigal, S., Shape sensitivity analysis of piezoelectric structures by the adjoint variable method, AIAA J. 29 (1991) 1313–1318 CrossRef
Hwang, J.K., Choi, C.H., Song, C.K., Lee, J.M., Robust LQG control of an all-clamped thin plate with piezoelectric actuators/sensors, IEEE/ASME Trans. Mechatron. 2 (1997) 205–212
M. Collet, L. Jezequel, Active control with piezo-electric layers optimization, J. Struct. Control. 1 (1995)
F. Fahroo, Y. Wang, Optimal location of piezoceramic actuators for vibration suppression of a flexible stucture, in Proc. the 36th IEEE Conference on Decision and Control, San Diego, CA, USA, 1997, pp. 1966–1971
Yang, S.Y., Huang, W.H., Is a collocated piezoelectric sensor/actuator pair feasible for an intelligent beam? J. Sound Vib. 216 (1998) 529–538 CrossRef
Monnier, P., Collet, M., Piranda, J., Definition of mechanical design parameters to optimize efficiency of Integral Force Feedback. Struct. Contr. Health Monit. 12 (2005) 65–89
Naillon, M., Coursant, R.H., Besnier, F., Analyse de structures piézoélectriques par une méthode d'éléments finis, Acta Elec. 25 (1983) 341–362
M. Collet, K.A. Cunefare, Modal synthesis and dynamical condensation methods for accurate piezoelectric systems impedance computation, J. Intell. Mater. Syst. Struct., on-line, 2008