Advertisement

Multibody System Dynamics

, Volume 30, Issue 1, pp 13–35 | Cite as

Active vibration control of spatial flexible multibody systems

  • Maria Augusta NetoEmail author
  • Jorge A. C. Ambrósio
  • Luis M. Roseiro
  • A. Amaro
  • C. M. A. Vasques
Article

Abstract

In this work a flexible multibody dynamics formulation of complex models including elastic components made of composite materials is extended to include piezoelectric sensors and actuators. The only limitation for the deformation of a structural member is that they must remain elastic and linear when described in a coordinate frame fixed to a material point or region of its domain. The flexible finite-element model of each flexible body is obtained referring the flexible body nodal coordinates to the body fixed frame and using a diagonalized mass description of the inertia in the mass matrix and on the gyroscopic force vector. The modal superposition technique is used to reduce the number of generalized coordinates to a reasonable dimension for complex shaped structural models of flexible bodies. The active vibration control of the flexible multibody components is implemented using an asymmetric collocated piezoelectric sensor/actuator pair. An electromechanically coupled model is taken into account to properly consider the surface-bonded piezoelectric transducers and their effects on the time and spatial response of the flexible multibody components. The electromechanical effects are introduced in the flexible multibody equations of motion by the use of beam and plate/shell elements, developed to this purpose. A comparative study between the classical control strategies, constant gain and amplitude velocity feedback, and optimal control strategy, linear quadratic regulator (LQR), is performed in order to investigate their effectiveness to suppress vibrations in structures with piezoelectric sensing and actuating patches.

Keywords

Piezoelectric material Active control Flexible multibody systems Elastic coupling Mode component synthesis 

References

  1. 1.
    Pritschow, G., Philipp, W.: Direct drives for high-dynamic machine tool axes. CIRP Ann. 39(1), 413–416 (1990) CrossRefGoogle Scholar
  2. 2.
    Ast, A., Eberhard, P.: Flatness-based control of parallel kinematics using multibody systems—simulation and experimental results. Arch. Appl. Mech. 76(3), 181–197 (2006) zbMATHCrossRefGoogle Scholar
  3. 3.
    Ambrósio, J., Neto, M.A., Leal, R.P.: Optimization of a complex flexible multibody systems with composite materials. Multibody Syst. Dyn. 18(2), 117–144 (2007) zbMATHCrossRefGoogle Scholar
  4. 4.
    Xianmin, Z., Changjian, S., Erdman, A.G.: Active vibration controller design and comparison study of flexible linkage mechanism systems. Mech. Mach. Theory 37(9), 985–997 (2002) zbMATHCrossRefGoogle Scholar
  5. 5.
    Cleghorn, W.L., Fenton, R.G., Tabarrok, B.: Optimum design of high-speed flexible mechanisms. Mech. Mach. Theory 16(4), 399–406 (1981) CrossRefGoogle Scholar
  6. 6.
    Xianmin, Z.: Integrated optimal design of flexible mechanism and vibration control. Int. J. Mech. Sci. 46(11), 1607–1620 (2004) zbMATHCrossRefGoogle Scholar
  7. 7.
    Trindade, M.A., Maio, C.E.B.: Multimodal passive vibration control of sandwich beams with shunted shear piezoelectric materials. Smart Mater. Struct. 17(5), 055015 (2008) CrossRefGoogle Scholar
  8. 8.
    Mohan, A., Singh, S., Saha, S.: A cohesive modeling technique for theoretical and experimental estimation of damping in serial robots with rigid and flexible links. Multibody Syst. Dyn. 23(4), 333–360 (2010) MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Ghazavi, A., Gordaninejad, F., Chalhoub, N.G.: Dynamic analysis of a composite-material flexible robot arm. Comput. Struct. 49(2), 315–327 (1993) zbMATHCrossRefGoogle Scholar
  10. 10.
    Liu, C., Tian, Q., Hu, H.: Dynamics of a large scale rigid–flexible multibody system composed of composite laminated plates. Multibody Syst. Dyn. 26(3), 283–305 (2011) zbMATHCrossRefGoogle Scholar
  11. 11.
    Sung, C.K., Chen, Y.C.: Vibration control of the elastodynamic response of high-speed flexible linkage mechanisms. J. Vib. Acoust. 113(1), 14–21 (1991) CrossRefGoogle Scholar
  12. 12.
    Behn, C.: Adaptive control of straight worms without derivative measurement. Multibody Syst. Dyn. 26(3), 213–243 (2011) MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Antos, P., Ambrósio, J.A.C.: A control strategy for vehicle trajectory tracking using multibody models. Multibody Syst. Dyn. 11(4), 365–394 (2004) zbMATHCrossRefGoogle Scholar
  14. 14.
    Seifried, R.: Two approaches for feedforward control and optimal design of underactuated multibody systems. Multibody Syst. Dyn. 27(1), 75–93 (2012) MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Liao, C.Y., Sung, C.K.: An elastodynamic analysis and control of flexible linkages using piezoceramic sensors and actuators. J. Mech. Des. 115(3), 658–665 (1993) CrossRefGoogle Scholar
  16. 16.
    Wang, X., Mills, J.K.: A FEM model for active vibration control of flexible linkages. In: Proceedings ICRA ’04. IEEE International Conference on Robotics and Automation, vol. 5, pp. 4308–4313 (2004) Google Scholar
  17. 17.
    Ambrosio, J.A.C., Nikravesh, P.E.: Elasto-plastic deformations in multibody dynamics. Nonlinear Dyn. 3(2), 85–104 (1992) CrossRefGoogle Scholar
  18. 18.
    Song, J.O., Haug, E.J.: Dynamic analysis of planar flexible mechanisms. Comput. Methods Appl. Mech. Eng. 24(3), 359–381 (1980) MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Neto, M.A., Ambrósio, J.A.C., Leal, R.P.: Sensitivity analysis of flexible multibody systems using composite materials components. Int. J. Numer. Methods Eng. 77(3), 386–413 (2009) zbMATHCrossRefGoogle Scholar
  20. 20.
    Das, M., Barut, A., Madenci, E.: Analysis of multibody systems experiencing large elastic deformations. Multibody Syst. Dyn. 23(1), 1–31 (2010) MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Simo, J.C., Vu-Quoc, L.: On the dynamics of flexible beams under large overall motions—the plane case: Part I. J. Appl. Mech. 53(4), 849–854 (1986) zbMATHCrossRefGoogle Scholar
  22. 22.
    von Dombrowski, S.: Analysis of large flexible body deformation in multibody systems using absolute coordinates. Multibody Syst. Dyn. 8(4), 409–432 (2002) MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Nachbagauer, K., Pechstein, A., Irschik, H., Gerstmayr, J.: A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation. Multibody Syst. Dyn. 26(3), 245–263 (2011) zbMATHCrossRefGoogle Scholar
  24. 24.
    Ambrósio, J.A.C., Gonçalves, J.P.C.: Complex flexible multibody systems with application to vehicle dynamics. Multibody Syst. Dyn. 6(2), 163–182 (2001) MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Eberhard, P., Dignath, F., Kübler, L.: Parallel evolutionary optimization of multibody systems with application to railway dynamics. Multibody Syst. Dyn. 9(2), 143–164 (2003) zbMATHCrossRefGoogle Scholar
  26. 26.
    Heirman, G., Naets, F., Desmet, W.: Forward dynamical analysis of flexible multibody systems using system-level model reduction. Multibody Syst. Dyn. 25(1), 97–113 (2011) MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Aarts, R., Meijaard, J., Jonker, J.: Flexible multibody modelling for exact constraint design of compliant mechanisms. Multibody Syst. Dyn. 27(1), 119–133 (2012) MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Ambrósio, J.: Efficient kinematic joint descriptions for flexible multibody systems experiencing linear and non-linear deformations. Int. J. Numer. Methods Eng. 56(12), 1771–1793 (2003) zbMATHCrossRefGoogle Scholar
  29. 29.
    Valentini, P., Pennestrì, E.: Modeling elastic beams using dynamic splines. Multibody Syst. Dyn. 25(3), 271–284 (2011) MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Sanborn, G., Shabana, A.: On the integration of computer aided design and analysis using the finite element absolute nodal coordinate formulation. Multibody Syst. Dyn. 22(2), 181–197 (2009) zbMATHCrossRefGoogle Scholar
  31. 31.
    Bauchau, O.A., Hodges, D.H.: Analysis of nonlinear multibody systems with elastic couplings. Multibody Syst. Dyn. 3(2), 163–188 (1999) zbMATHCrossRefGoogle Scholar
  32. 32.
    Neto, M.A., Ambrósio, J.A.C., Leal, R.P.: Flexible multibody systems models using composite materials components. Multibody Syst. Dyn. 12(4), 385–405 (2004) zbMATHCrossRefGoogle Scholar
  33. 33.
    Neto, A.M., Yu, W., Roy, S.: Two finite elements for general composite beams with piezoelectric actuators and sensors. In: Finite Elements in Analysis and Design, vol. 45, pp. 295–304 (2009) Google Scholar
  34. 34.
    Neto, M.A., Leal, R.P., Yu, W.: A triangular finite element with drilling degrees of freedom for static and dynamic analysis of smart laminated structures. Comput. Struct. 108–109, 61–74 (2012) CrossRefGoogle Scholar
  35. 35.
    Vasques, C.M.A., Dias Rodrigues, J.: Active vibration control of smart piezoelectric beams: comparison of classical and optimal feedback control strategies. Comput. Struct. 84(22–23), 1402–1414 (2006) CrossRefGoogle Scholar
  36. 36.
    Kwak, M.K., Heo, S.: Active vibration control of smart grid structure by multiinput and multioutput positive position feedback controller. J. Sound Vib. 304(1–2), 230–245 (2007) CrossRefGoogle Scholar
  37. 37.
    Reddy, J.N.: Mechanics of Laminated Composite Plates: Theory and Analysis. CRC Press, Boca Raton (1997) zbMATHGoogle Scholar
  38. 38.
    Zemčík, R., Rolfes, R., Rose, M., Teßmer, J.: High-performance four-node shell element with piezoelectric coupling for the analysis of smart laminated structures. Int. J. Numer. Methods Eng. 70(8), 934–961 (2007) zbMATHCrossRefGoogle Scholar
  39. 39.
    Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method. Butterwort-Heinemann, Woburn (2000) zbMATHGoogle Scholar
  40. 40.
    Chevallier, G., et al.: A benchmark for free vibration and effective coupling of thick piezoelectric smart structures. Smart Mater. Struct. 17(6), 065007 (2008) CrossRefGoogle Scholar
  41. 41.
    Cook, R.: Concepts and Applications of Finite Element Analysis. Wiley, New York (1987) Google Scholar
  42. 42.
    Craig, R.R.: Structural Dynamics: An Introduction to Computer Methods. Wiley, New York (1981) Google Scholar
  43. 43.
    Cuadrado, J., Cardenal, J., Bayo, E.: Modeling and solution methods for efficient real-time simulation of multibody dynamics. Multibody Syst. Dyn. 1(3), 259–280 (1997) MathSciNetzbMATHCrossRefGoogle Scholar
  44. 44.
    Nikravesh, P.E.: Computer Aided Analysis of Mechanical Systems. Prentice-Hall, Englewood Cliffs (1988) Google Scholar
  45. 45.
    Pereira, M.S., Proença, P.L.: Dynamic analysis of spatial flexible multibody systems using joint co-ordinates. Int. J. Numer. Methods Eng. 32(8), 1799–1812 (1991) zbMATHCrossRefGoogle Scholar
  46. 46.
    Yoo, W.S., Haug, E.J.: Dynamic of flexible mechanical systems using vibration and static correction modes. J. Mech. Transm. Autom. Des. 108, 315–322 (1986) CrossRefGoogle Scholar
  47. 47.
    Cavin, R.K., Dusto, A.R.: Hamilton’s principle: finite element methods and flexible body dynamics. AIAA J. 15(12), 1684–1690 (1977) zbMATHCrossRefGoogle Scholar
  48. 48.
    Balas, M.: Feedback control of flexible systems. IEEE Trans. Autom. Control 23(4), 673–679 (1978) zbMATHCrossRefGoogle Scholar
  49. 49.
    Meirovitch, L.: Dynamics and Control of Structures. Wiley, New York (1990) Google Scholar
  50. 50.
    Franklin, G.F., Powell, J.D., Emami-Naeini, A.: Feedback Control of Dynamic Systems, 4th edn. Prentice-Hall, Upper Saddle River (2002) Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Maria Augusta Neto
    • 1
    Email author
  • Jorge A. C. Ambrósio
    • 2
  • Luis M. Roseiro
    • 3
  • A. Amaro
    • 1
  • C. M. A. Vasques
    • 4
  1. 1.Departamento de Engenharia Mecânica, Faculdade de Ciência e TecnologiaUniversidade de Coimbra (Polo II)CoimbraPortugal
  2. 2.Instituto de Engenharia MecânicaInstituto Superior TécnicoLisboaPortugal
  3. 3.Departamento de Engenharia MecânicaInstituto Superior de Engenharia de CoimbraCoimbraPortugal
  4. 4.INEGI–Instituto de Engenharia Mecânica e Gestão IndustrialUniversidade do PortoPortoPortugal

Personalised recommendations