Smart Structures and Systems

  • 제17권5호
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  • Pages.773-793
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  • 2016
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  • 1738-1584(pISSN)
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  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

A controllability-based formulation for the topology optimization of smart structures

  • Goncalves, Juliano F. (Department of Mechanical Engineering, Federal University of Rio Grande do Sul) ;
  • Fonseca, Jun S.O. (Department of Mechanical Engineering, Federal University of Rio Grande do Sul) ;
  • Silveira, Otavio A.A. (Department of Civil Engineering, Federal University of Santa Catarina)
  • 투고 : 2015.04.21
  • 심사 : 2016.02.16
  • 발행 : 2016.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

This work presents a methodology to distribute piezoelectric material for structural vibration active control. The objective is to design controlled structures with actuators which maximizes the system controllability. A topology optimization was formulated in order to distribute two material phases in the domain: a passive linear elastic material and an active linear piezoelectric material. The objective is the maximization of the smallest eigenvalue of the system controllability Gramian. Analytical sensitivities for the finite element model are derived for the objective functions and constraints. Results and comparisons with previous works are presented for the vibration control of a two-dimensional short beam.

키워드

참고문헌

  1. Allik, H. and Hughes, T.J.R. (1995), "Finite element method for piezoelectric vibration", Int. J. Numer. Meth. Eng., 2, 151-157.
  2. Balas, M.J. (1978), "Feedback control of flexible systems", IEEE T. Automat. Contr., 23(4), 673-679. https://doi.org/10.1109/TAC.1978.1101798
  3. Bartels, R.H. and Stewart, G.W. (1972), "Solution of the matrix equation ax+ xb= c [f4]", Commun. ACM, 15(9), 820-826. https://doi.org/10.1145/361573.361582
  4. Bendsoe, M.P. (1989), "Optimal shape design as a material distribution problem", Struct. Optimization, 1, 193-202. https://doi.org/10.1007/BF01650949
  5. Bendsoe, M.P. and Sigmund, O. (1999), "Material interpolation schemes in topology optimization", Arch. Appl. Mech., 69, 635-654. https://doi.org/10.1007/s004190050248
  6. Bendsoe, M.P. and Kikuchi, N. (1988), "Generating optimal topologies in structural design using a homogenization method", Comput. Method. Appl. M., 71(2), 197-224. https://doi.org/10.1016/0045-7825(88)90086-2
  7. Burl, J.B. (1999), Linear Optimal Control, Addison-Wesley, California, USA.
  8. Gawronski, W. (2004), Advanced Structural Dynamics and Active Control of Structures, Springer-Verlag, New York, USA.
  9. Gawronski, W. and Lim, K.B. (1996), "Balanced actuator and sensor placement for flexible structures", Int. J. Control, 65, 131-145. https://doi.org/10.1080/00207179608921690
  10. Gupta, V., Sharma, M., Thakur, N. and Singh, S.P. (2011), "Active vibration control of a smart plate using a piezoelectric sensor-actuator pair at elevated temperatures", Smart Mater. Struct., 20(10), 105023. https://doi.org/10.1088/0964-1726/20/10/105023
  11. Hac, A. and Liu, L. (1993), "Sensor and actuator location in motion control of flexible structures", J. Sound Vib., 167(2), 239-261. https://doi.org/10.1006/jsvi.1993.1333
  12. Hamdan, A.M.A. and Nayfeh, A.H. (1989), "Measures of modal controllability and observability for first and second-order linear systems", J. Guid. Control. Dynam., 12(3), 421-428. https://doi.org/10.2514/3.20424
  13. Kim, J.E., Kim, D.S., Ma, P.S. and Kim, Y.Y. (2010) "Multi-physics interpolation for the topology optimization of piezoelectric systems", Comput. Method. Appl. M., 199(49), 3153-3168. https://doi.org/10.1016/j.cma.2010.06.021
  14. Kim, Y. and Junkins, J.L. (1991), "Measure of controllability for actuator placement", J. Guid. Control. Dynam., 14, 895-902. https://doi.org/10.2514/3.20729
  15. Kumar, K.R. and Narayanan, S. (2008), "Active vibration control of beams with optimal placement of piezoelectric sensor/actuator pairs", Smart Mater. Struct., 17(5), 055008. https://doi.org/10.1088/0964-1726/17/5/055008
  16. Leleu, S., Abou-Kandil, H. and Bonnassieux, Y. (2001), "Piezoelectric actuators and sensors location for active control of flexible structures", IEEE T. Instrum. Meas, 50(6), 1577-1582. https://doi.org/10.1109/19.982948
  17. Meirovitch, L. (1990), Dynamics and Control of Structures, John Wiley & Sons, New York, USA.
  18. Onoda, J. and Haftka, R.T. (1987), "An approach to structure/control simultaneous optimization for large flexible spacecraft", AIAA J., 25(8), 1133-1138. https://doi.org/10.2514/3.9754
  19. Ou, J.S. and Kikuchi, N. (1996), "Integrated optimal structural and vibration control design", Struct.Optimization, 12(4), 209-216. https://doi.org/10.1007/BF01197358
  20. Preumont, A. (2002), Vibration Control of Active Structures, An Introduction, Kluwer Academic Publisher, Dordrecht, The Netherlands.
  21. Rubio, W.M., Silva, E.C.N. and Paulino, G.H. (2009), "Toward optimal design of piezoelectric transducers based on multifunctional and smoothly graded hybrid material systems", J. Intel. Mat. Syst. Str., 20(14), 1725-1746. https://doi.org/10.1177/1045389X09337085
  22. Ruiz, D., Bellido, J.C., Donoso, A. and Sanchez-Rojas, J.L. (2013), "Design of in-plane piezoelectric sensors for static response by simultaneously optimizing the host structure and the electrode profile", Struct. Multidiscip. O., 48(5), 1023-1026. https://doi.org/10.1007/s00158-013-0923-8
  23. Seyranian, A.P., Lund, E. and Olhoff, N. (1994), "Multiple eigenvalues in structural optimization problems", Struct. Optimization, 8(4), 207-227. https://doi.org/10.1007/BF01742705
  24. Sigmund, O. (1997), "On the design of compliant mechanisms using topology optimization", Mech. Struct. Machines, 25(4), 493-524. https://doi.org/10.1080/08905459708945415
  25. Sigmund, O. and Petersson, J. (1998), "Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local-minima", Struct. Optimization, 16(1), 68-75. https://doi.org/10.1007/BF01214002
  26. Silva, E.C.N. and Kikuchi, N. (1999), "Design of piezoelectric transducers using topology optimization", Smart Mater. Struct., 8(3), 350. https://doi.org/10.1088/0964-1726/8/3/307
  27. Silveira, O.A.A., Fonseca, J.S.O. and Santos, I.F. (2015), "Actuator topology design using the controllability gramian", Struct. Multidiscip.O., 51(1), 145-157. https://doi.org/10.1007/s00158-014-1121-z
  28. Sohn, J.W., Choi, S. and Kim, H.S. (2011), "Vibration control of smart hull structure with optimally placed piezoelectric composite actuators", Int. J. Mech. Sci., 53(8), 647-659. https://doi.org/10.1016/j.ijmecsci.2011.05.011
  29. Takezawa, A., Kitamura, M., Vatanabe, S.L. and Silva, E.C.N. (2014), "Design methodology of piezoelectric energy-harvesting skin using topology optimization", Struct. Multidiscip.O., 49(2), 281-297. https://doi.org/10.1007/s00158-013-0974-x
  30. Takezawa, A., Makihara, K., Kogiso, N. and Kitamura, M. (2014), "Layout optimization methodology of piezoelectric transducers in energy-recycling semi-active vibration control systems". J. Sound Vib., 333(2), 327-344. https://doi.org/10.1016/j.jsv.2013.09.017
  31. Takezawa, A., Nishiwaki, S., Kitamura, M. and Silva, E.C.N. (2010), "Topology optimization for designing strain-gauge load cells", Struct. Multidiscip.O., 42 (3), 387-402. https://doi.org/10.1007/s00158-010-0491-0
  32. Taylor, R.L., Beresford, P.J. and Wilson, E.L. (1976), "A non-conforming element for stress analysis", Int. J. Numer. Methods in Engineering, 10(6), 1211-1219. https://doi.org/10.1002/nme.1620100602
  33. Vasques, C.M.A. and Rodrigues, J.D. (2006), "Active vibration control of smart piezoelectric beams: Comparasion of classical and optimal feedback control strategies", Comput. Struct., 84, 1402-1414. https://doi.org/10.1016/j.compstruc.2006.01.026
  34. Wang, Q. and Wang, C.M. (2001), "A controllability index for optimal design of piezoelectric actuators in vibration control of beam structures", J. Sound Vib., 242(3), 507-518. https://doi.org/10.1006/jsvi.2000.3357
  35. Wu, B., Xu, Z. and Li, Z. (2007), "A note on computing eigenvector derivatives with distinct and repeated eigenvalues", Commun. Numer. Meth. En., 23, 241-251.
  36. Zhang, X. and Kang, Z. (2014), "Dynamic topology optimization of piezoelectric structures with active control for reducing transient response", Computer Methods in Applied Mechanics and Engineering, 281, 200-219. https://doi.org/10.1016/j.cma.2014.08.011

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