Rigid Body, Flexible Body, and Micro Electromechanical Systems

  • Rochdi Merzouki
  • Arun Kumar Samantaray
  • Pushparaj Mani Pathak
  • Belkacem Ould Bouamama
Chapter

Abstract

Planar multibody systems, and revolute and prismatic joints with clearance and friction are initially modeled in this chapter with Rapson slide and Andrew’s mechanism as two examples. For modeling spatial multibody systems, the concepts of noninertial reference frame, Euler angles, and coordinate transformations, etc., are introduced. Hydraulically actuated leg of a Stewart platform and spinning top are modeled as examples. Flexible body systems such as beams, beam columns, composite beams, and bimetallic strips are modeled through spatial discretization and lumped parameter approximation. A thorough treatment is given to modeling of piezoelectric actuators and sensors. Thereafter, models for various microelectromechanical systems (MEMS) like micromirrors, micromotors, magnetohydrodynamic micropumps, wet shape memory alloy (SMA) actuator, and energy harvesting systems, etc. are developed. Further, models of rotor-bearing systems with rolling element, journal, and magnetic bearings are developed with special emphasis on active magnetic bearing model. The importance of integrated modeling is shown by considering the case of Sommerfeld effect in a rotor dynamic system and its control through shape memory alloy actuators.

References

  1. 1.
    S. Ahmed, H.M. Lankarani, M.F.O.S. Pereira, Frictional impact analysis in open-loop multibody mechanical systems. Trans. ASME J. Mech. Des. 121(1), 119–127 (1999)CrossRefGoogle Scholar
  2. 2.
    B.J. Aleck, Thermal stresses in a rectangular plate clamped along an edge. ASME J. Appl. Mech. 16, 118–122 (1949)MathSciNetMATHGoogle Scholar
  3. 3.
    W.T. Ang, F.A. Garmn, P.K. Khosla, C.N. Riviere, Modeling rate-dependent hysteresis in piezoelectric actuators, in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, Nevada, 2003Google Scholar
  4. 4.
    K.J. Astrom, C. Canudas de Wit, H. Olsson, P. Lischinsky, A new model for the control of systems with friction. IEEE Trans. Autom. Control 40(3), 419–425 (1995)MathSciNetCrossRefGoogle Scholar
  5. 5.
    J.M. Balthazar, D.T. Mook, H.I. Weber, R.M.L.R.F. Brasil, A. Fenili, D. Belato, J.L.P. Felix, An overview on non-ideal vibrations. Meccanica 38, 613–621 (2003)Google Scholar
  6. 6.
    S. Behzadipour, A. Khajepour, Causality in vector bond graphs and its application to modeling of multi-body dynamic systems. Simul. Model. Pract. Theory 14(3), 279–295 (2006)CrossRefGoogle Scholar
  7. 7.
    T.K. Bera, A.K. Samantaray, Consistent bond graph modeling of planar multibody systems. World J. Model. Simul. 7(3), 173–178 (2011)Google Scholar
  8. 8.
    A.N. Bercin, M. Tanaka, Coupled flexural-torsional vibrations of Timoshenko beams. J. Sound Vib. 207(1), 47–59 (1997)CrossRefGoogle Scholar
  9. 9.
    R. Bhattacharyya, A. Mukherjee, A.K. Samantaray, Harmonic oscillations of non-conservative, asymmetric, two-degree-of-freedom systems. J. Sound Vib. 264, 973–980 (2003)CrossRefGoogle Scholar
  10. 10.
    D. Biolek, Z. Biolek, V. Biolkova, Spice modelling of memcapacitor. Elect. Lett. 46(7), 520–522 (2010)CrossRefGoogle Scholar
  11. 11.
    I.I. Blekhman, Vibrational Mechanics: Nonlinear Dynamic Effects, General Approach, Applications (World Scientific, Singapore, 2000)CrossRefGoogle Scholar
  12. 12.
    W. Borutzky, Bond Graph Methodology—Development and Analysis of Multidisciplinary Dynamic System Models (Springer, Heidelberg, 2010)Google Scholar
  13. 13.
    W. Borutzky, B. Barnard, J. Thoma, Describing bond graph models of hydraulic components in Modelica. Math. Comput. Simul. 53, 381–387 (2000)CrossRefGoogle Scholar
  14. 14.
    W. Borutzky, B. Barnard, J. Thoma, An orifice flow model for laminar and turbulent conditions. Simul. Model. Pract. Theory 10, 141–152 (2002)MATHCrossRefGoogle Scholar
  15. 15.
    N.M. Bou-Rabee, J.E. Marsden, L.A. Romero, Tippe top inversion as a dissipation-induced instability. SIAM J. Appl. Dyn. Syst. 3(3), 352–377 (2004)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    A. Boukari, Piezoelectric actuators modeling for complex systems control. Ph.D. thesis, Arts et Mtiers ParisTech, 2010Google Scholar
  17. 17.
    A.F. Boukari, G. Moraru, J.C. Carmona, Malburet F, User-oriented simulation models of piezo-bar actuators: part I and part II, in Proceedings of IDETC/CIE 2009, ASME 2009 International Design Engineering Technical Conferences& International Conference on Mechatronic and Embedded Systems and Applications, San Diego, USA, 2009Google Scholar
  18. 18.
    T.A. Bowers, Modeling, simulation and control of a polypyrrole-based conducting polymer actuator. Master’s thesis, Arizona State University, 2004Google Scholar
  19. 19.
    P.C. Breedveld, An alternative model for static and dynamic friction in dynamic system simulation, in IFAC-Conference on Mechatronic Systems, vol. 2, pp. 717–722, 2000Google Scholar
  20. 20.
    M.D. Bryant, S. Lee, Resistive field bond graph models for hydrodynamically lubricated bearings. Proc. IMechE Part I: J. Syst. Control Eng. 218(8), 645–654 (2004)CrossRefGoogle Scholar
  21. 21.
    M. Calin, N. Chaillet, J. Agnus, A. Bourjault, Design of cooperative microrobots with impedance optimization, in IEEE International Conference on Intelligent Robots and Systems, pp. 1312–1317, 1997Google Scholar
  22. 22.
    R. Changhai, S. Lining, Hysteresis and creep compensation for piezoelectric actuator in open-loop operation. Sens. Actuator A 122, 124–130 (2005)CrossRefGoogle Scholar
  23. 23.
    C.J. Chen, Introduction to Scanning Tunneling Microscopy (Oxford University Press, Oxford 1993)Google Scholar
  24. 24.
    R. Chhabra, M. Reza Emami, Holistic system modeling in mechatronics. Mechatronics 21(1), 166–175 (2011)CrossRefGoogle Scholar
  25. 25.
    L.O. Chua, Memristor-the missing circuit element. IEEE Trans. Circ. Theory 18, 507–519 (1971)CrossRefGoogle Scholar
  26. 26.
    L.O. Chua, S.M. Kang, Memristive devices and systems. Proc. IEEE 64(2), 209–223 (1976)MathSciNetCrossRefGoogle Scholar
  27. 27.
    J. Compos, M. Crawford, R. Longoria, Rotordynamic modeling using bond graphs: modeling the jeffcott rotor. IEEE Trans. Magn. 41(1), 274–280 (2005)CrossRefGoogle Scholar
  28. 28.
    S.H. Crandall, The effect of damping on the stability of gyroscopic pendulums. Zeitschrift fur Angewandte Mathematik und Physik 46, S761–S780 (1995)MathSciNetMATHGoogle Scholar
  29. 29.
    D. Croft, G. Shed, S. Devasia, Creep, hysteresis, and vibration compensation for piezoactuators: atomic force microscopy application. ASME J. Dyn. Syst. Meas. Control 123, 3543 (2001)CrossRefGoogle Scholar
  30. 30.
    Y. Cui, R.X. Gao, D. Yang, D.O. Kazmer, A bond graph approach to energy efficiency analysis of a self-powered wireless pressure sensor. Smart Struct. Syst. 3(1), 1–22 (2007)Google Scholar
  31. 31.
    V. Damic, Modelling flexible body systems: a bond graph component model approach. Math. Comput. Model. Dyn. Syst. 12(2–3), 175–187 (2006)Google Scholar
  32. 32.
    S.S. Dasgupta, A.K. Samantaray, R. Bhattacharyya, Stability of an internally damped non-ideal flexible spinning shaft. Int. J. Non-Linear Mech. 45(3), 286–293 (2010)CrossRefGoogle Scholar
  33. 33.
    M. Di Ventra, Y.V. Pershin, L.O. Chua, Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc. IEEE 97(10), art. no. 5247127:1717–1724 (2009)Google Scholar
  34. 34.
    M. Di Ventra, Y.V. Pershin, L.O. Chua, Putting memory into circuit elements: memristors, memcapacitors, and meminductors. Proc. IEEE 97(8), art. no. 5109686:1371–1372 (2009)Google Scholar
  35. 35.
    M.F. Dimentberg, L. McGovern, R.L. Norton, J. Chapdelaine, R. Harrison, Dynamics of an unbalanced shaft interacting with a limited power supply. Nonlinear Dyn. 13, 171–187 (1997)MATHCrossRefGoogle Scholar
  36. 36.
    P. Dupont, V. Hayward, B. Armstrong, F. Altpeter, Single state elasto-plastic friction models. IEEE Trans. Autom. Control 47(5), 187–192 (2002)MathSciNetCrossRefGoogle Scholar
  37. 37.
    M. Eckert, The Sommerfeld effect: theory and history of a remarkable resonance phenomenon. Eur. J. Phys. 17(5), 285–289 (1996)CrossRefGoogle Scholar
  38. 38.
    J.W. Eischen, C. Chung, J.H. Kim, Realistic modeling of edge effect stresses in bimaterial elements. ASME J. Elect. Packag. 112, 16–23 (1990)CrossRefGoogle Scholar
  39. 39.
    J.J. Epps, I. Chopra, Comparative evaluation of shape memory alloy constitutive models with test data, in Collection of Technical Papers—AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, vol. 2, pp. 1425–1437, 1997Google Scholar
  40. 40.
    T. Ersal, H.K. Fathy, J.L. Stein, Structural simplification of modular bond-graph models based on junction inactivity. Simul. Model. Pract. Theory 17(1), 175–196 (2009)CrossRefGoogle Scholar
  41. 41.
    J.D. Ertel, S.A. Mascaro, Dynamic thermomechanical modeling of a wet shape memory alloy actuator. J. Dyn. Syst. Meas. Control Trans. ASME 132(5), 1–9 (2010)CrossRefGoogle Scholar
  42. 42.
    B. Eryilmaz, B.H. Wilson, Unified modeling and analysis of a proportional valve. J. Franklin Inst. 343, 48–68 (2006)MATHCrossRefGoogle Scholar
  43. 43.
    A.P. Filippov, Vibrations of Mechanical Systems (National Lending Library for Science and Technology, Boston Spa, Yorkshire, England, 1971)Google Scholar
  44. 44.
    L. Flemming, S. Mascaro, Wet SMA actuator array with matrix vasoconstriction device, in Proceedings of the 2005 ASME International Mechanical Engineering Congress and Exposition, pp. 1751–1758, 2005Google Scholar
  45. 45.
    P. Flores, Modeling and simulation of wear in revolute clearance joints in multibody systems. Mech. Mach. Theory 44(6), 1211–1222 (2009)MathSciNetMATHCrossRefGoogle Scholar
  46. 46.
    P. Flores, J. Ambrosio, J.C. Pimenta Claro, H.M. Lankarani, Kinematics and Dynamics of Multibody Systems with Imperfect Joints: Models and Case Studies (Springer, Berlin, 2008)MATHGoogle Scholar
  47. 47.
    A.M. Flynn, S.R. Sanders, Fundamental limits on energy transfer and circuit considerations for piezoelectric transformers. IEEE Trans. Power Electr. 17(1), 8–14 (2002)CrossRefGoogle Scholar
  48. 48.
    R.X. Gao, Y. Cui, Vibration-based sensor powering for manufacturing process monitoring. Trans. North Am. Manuf. Res. Inst. SME 33, 335–342 (2005)Google Scholar
  49. 49.
    P.J. Gawthrop, B. Bhikkaji, S.O.R. Moheimani, Physical-model-based control of a piezoelectric tube for nano-scale positioning applications. Mechatronics 20, 74–84 (2010)CrossRefGoogle Scholar
  50. 50.
    G. Genta, Dynamics of Rotating Systems (Springer, Heidelberg, 2005)Google Scholar
  51. 51.
    P.J. Gilgunn, Large angle micro-mirror arrays in CMOS-MEMS. Master’s thesis, Carnegie Mellon University, 2006Google Scholar
  52. 52.
    M. Goldfarb, N. Celanovic, A lumped parameter electromechanical model for describing the nonlinear behavior of piezoelectric actuators. J. Dyn. Syst. Meas. Control Trans. ASME 119(3), 478–485 (1997)MATHCrossRefGoogle Scholar
  53. 53.
    O. Gomis-Bellmunt, F. Ikhouane, P. Castell-Vilanova, J. Bergas-Jan, Modeling and validation of a piezoelectric actuator. Electron. Eng. 89, 629–638 (2007)CrossRefGoogle Scholar
  54. 54.
    B. Halder, A. Mukherjee, R. Karmakar, Theoretical and experimental studies on squeeze film stabilizers for flexible rotor-bearing systems using newtonian and viscoelastic lubricants. Trans. ASME J. Vib. Acoust. Stress Reliab. Des. 112(4), 473–482 (1990)Google Scholar
  55. 55.
    Y.-Y. He, S. Oi, F.-L. Chu, H.-X. Li, Vibration control of a rotor-bearing system using shape memory alloy: I. Theory. Smart Mater. Struct. 16(1), 114–121 (2007)CrossRefGoogle Scholar
  56. 56.
    Y.-Y. He, S. Oi, F.-L. Chu, H.-X. Li, Vibration control of a rotor-bearing system using shape memory alloy: II. Experimental study. Smart Mater. Struct. 16(1), 122–127 (2007)CrossRefGoogle Scholar
  57. 57.
    R. Holmes, The effect of sleeve bearings on the vibration of rotating shafts. Tribology 5(4), 161–168 (1972)CrossRefGoogle Scholar
  58. 58.
    L. Howald, H. Rudin, H.J. Guentherodt, Piezoelectric inertial stepping motor with spherical rotor. Rev. Sci. Instrum. 63(8), 3909–3912 (1992)CrossRefGoogle Scholar
  59. 59.
    D. Hrovat, J. Asgari, M. Fodor, in Automotive Mechatronic Systems, Mechatronic Systems Techniques and Applications: Transportation and Vehicular Systems, vol. 2 (Gordon and Breach Science Publishers, Amsterdam, 2000), pp. 1–98Google Scholar
  60. 60.
    M. Hubbard, Whirl dynamics of pendulous flywheels using bond graphs. J. Franklin Inst. 308(4), 505–521 (1979)MathSciNetCrossRefGoogle Scholar
  61. 61.
    T. Ikeda, Fundamentals of Piezoelectricity (Oxford Science Publications, Oxford, 1996)Google Scholar
  62. 62.
    T. Ikeda, F.A. Nae, H. Naito, Y. Matsuzaki, Constitutive model of shape memory alloys for unidirectional loading considering inner hysteresis loops. Smart Mater. Struct. 13, 916–925 (2004)CrossRefGoogle Scholar
  63. 63.
    T. Iwatsubo, H. Kanki, R. Kawai, Vibration of asymmetric rotor through critical speed with limited power supply. J. Mech. Eng. Sci. 14(3), 184–194 (1972)CrossRefGoogle Scholar
  64. 64.
    D. Karnopp, Computer simulation of stick-slip friction in mechanical dynamic systems. J. Dyn. Syst. Meas. Control Trans. ASME 107(1), 100–103 (1985)CrossRefGoogle Scholar
  65. 65.
    D.C. Karnopp, D.L. Margolis, R.C. Rosenberg, System Dynamics: Modeling and Simulation of Mechatronic Systems (Wiley, New York, 2000)Google Scholar
  66. 66.
    D.C. Karnopp, Power-conserving transformations: physical interpretations and applications using bond graphs. J. Franklin Inst. 288(3), 175–201 (1969)CrossRefGoogle Scholar
  67. 67.
    D.C. Karnopp, D.L. Margolis, Analysis and simulation of planar mechanism systems using bond graphs. J. Mech. Des. 101, 187–191 (1979)CrossRefGoogle Scholar
  68. 68.
    S. Karunanidhi, M. Singaperumal, Mathematical modelling and experimental characterization of a high dynamic servo valve integrated with piezoelectric actuator. Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng. 224(4), 419–435 (2010)CrossRefGoogle Scholar
  69. 69.
    O. Kavehei, A. Iqbal, Y.S. Kim, K. Eshraghian, S.F. Al-Sarawi, D. Abbott, The fourth element: characteristics, modelling and electromagnetic theory of the memristor. Proc. R. Soc. A 466(2120), 2175–2202 (2010)MathSciNetMATHCrossRefGoogle Scholar
  70. 70.
    O.N. Kirillov, Destabilization paradox due to breaking the hamiltonian and reversible symmetry. Int. J. Non-Linear Mech. 42, 71–87 (2007)MathSciNetMATHCrossRefGoogle Scholar
  71. 71.
    M. Krems, Y.V. Pershin, M. Di Ventra, Ionic memcapacitive effects in nanopores. Nano Lett. 10(7), 2674–2678 (2010)CrossRefGoogle Scholar
  72. 72.
    V. Lampaert, Modelling and control of dry sliding friction in mechanical systems. Ph.D. thesis, Katholieke Universiteit Leuven, 2003Google Scholar
  73. 73.
    A. Lasia, Electrochemical Impedance Spectroscopy and Its Applications. Modern Aspects of Electrochemistry, vol. 32, chapter 2 (Kluwer Academic/Plenum Pub, New York, 1999), p. 143Google Scholar
  74. 74.
    D.E. Lee, Development of micropump for microfluidic applications. Ph.D. thesis, Louisiana State University, 2007Google Scholar
  75. 75.
    F.-S. Lee, T.J. Moon, G.Y. Masada, Extended bond graph reticulation of piezoelectric continua. J. Dyn. Sys. Meas. Control 117(1), 1–7 (1995)Google Scholar
  76. 76.
    A.W. Lees, S. Jana, D.J. Inman, M.P. Cartmell, The control of bearing stiffness using shape memory. in 4th International Symposium on Stability Control of Rotating Machinery (ISCORMA-4), Calgary, Alberta, Canada, 27–30 August 2007Google Scholar
  77. 77.
    C. Liang, C.A. Rogers, One dimensional thermomechanical constitutive relations for shape memory material. J. Intell. Mater. Struct. 1, 207–234 (1990)CrossRefGoogle Scholar
  78. 78.
    D.L. Margolis, G.E. Young, Reduction of models of large scale lumped structures using normal modes and bond graphs. J. Franklin Inst. 304(1), 65–79 (1977)MATHCrossRefGoogle Scholar
  79. 79.
    D.L. Margolis, Bond graphs and the exploitation of power conserving transformations. Comput. Programs Biomed. 8(3–4), 165–170 (1978)Google Scholar
  80. 80.
    W. Marquis-favre, E. Bideaux, S. Scavarda, A planar mechanical library in the AMESIM simulation software. Part I: Formulation of dynamics equations. Simul. Model. Pract. Theory 14, 25–46 (2006)CrossRefGoogle Scholar
  81. 81.
    W. Marquis-favre, E. Bideaux, S. Scavarda, A planar mechanical library in the AMESIM simulation software. Part II: Library composition and illustrative example. Simul. Model. Pract. Theory 14, 95–111 (2006)CrossRefGoogle Scholar
  82. 82.
    K. Medjaher, A.K. Samantaray, B. Ould Bouamama, Bond graph model of a vertical U-tube steam condenser coupled with a heat exchanger. Simul. Model. Pract. Theory 17(1), 228–239 (2009)CrossRefGoogle Scholar
  83. 83.
    H.E. Merrit, Hydraulic Control Systems (Wiley, New York, 1967)Google Scholar
  84. 84.
    W. Moon, I.J. Busch-Vishniac, Finite element equivalent bond graph modeling with application to the piezoelectric thickness vibrator. J. Acoust. Soc. Am. 93, 3496–3506 (1993)CrossRefGoogle Scholar
  85. 85.
    W. Moon, I.J. Busch-Vishniac, Modeling of piezoelectric ceramic vibrators including thermal effects: Part III. Bond graph model for one dimensional heat conduction. J. Acoust. Soc. Am. 101, 1398–1407 (1997)CrossRefGoogle Scholar
  86. 86.
    W. Moon, I.J. Busch-Vishniac, Modeling of piezoelectric ceramic vibrators including thermal effects. Part IV: development and experimental evaluation of a bond graph model of the thickness vibrator. J. Acoust. Soc. Am. 101, 1408–1429 (1997)CrossRefGoogle Scholar
  87. 87.
    C. Morin, Z. Moumni, W. Zaki, A constitutive model for shape memory alloys accounting for thermomechanical coupling. Int. J. Plast. 27, 748–767 (2011)MATHCrossRefGoogle Scholar
  88. 88.
    C. Morin, Z. Moumni, W. Zaki, Thermomechanical coupling in shape memory alloys under cyclic loadings: Experimental analysis and constitutive modeling. Int. J. Plast. 27, 1959–1980 (2011)MATHCrossRefGoogle Scholar
  89. 89.
    A. Mukherjee, Effect of bi-phase lubricants on dynamics of rigid rotors. Trans. ASME J. Lubr. Tech. 105, 29–38 (1983)CrossRefGoogle Scholar
  90. 90.
    A Mukherjee, R. Karmakar, Modelling and Simulation of Engineering Systems through Bond Graphs (Alpha Sciences International, Pangbourne, UK, 2000)Google Scholar
  91. 91.
    A. Mukherjee, R. Karmakar, A.K. Samantaray, Bond Graph in Modeling, Simulation and Fault Identification (CRC Press, Boca Raton, 2006) ISBN: 978-8188237968, 1420058657Google Scholar
  92. 92.
    A. Mukherjee, R. Karmakar, A.K. Samantaray, Modelling of basic induction motors and source loading in rotor-motor systems with regenerative force field. Simul. Pract. Theory 7(5), 563–576 (1999)CrossRefGoogle Scholar
  93. 93.
    A. Mukherjee, V. Rastogi, A. Dasgupta, Extension of lagrangian-hamiltonian mechanics for continuous systems-investigation of dynamics of a one-dimensional internally damped rotor driven through a dissipative coupling. Nonlinear Dyn. 58(1–2), 107–127 (2009)Google Scholar
  94. 94.
    A. Mukherjee, S. Sengupta, Active stabilization of rotors with circulating forces due to spinning dissipation. J. Vib. Control 17(10), 1509–1524 (2011)MathSciNetCrossRefGoogle Scholar
  95. 95.
    J. Mullins, Memristor minds. New Sci. 4, 42–45 (2009)Google Scholar
  96. 96.
    K. Nagaya, S. Takeda, Y. Tsukui, T. Kumaido, Active control method for passing through critical speeds of rotating shafts by changing stiffnesses of the supports with use of memory metals. J. Sound Vib. 113(2), 307–315 (1987)Google Scholar
  97. 97.
    M. Nakhaeinejad, M.D. Bryant, Dynamic modeling of rolling element bearings with surface contact defects using bond graphs. J. Tribol. 133(1) art. no. 011102 (2011)Google Scholar
  98. 98.
    M. Nakhaeinejad, S. Lee, M.D. Bryant, Finite element bond graph model of rotors, in 2010 Spring Simulation Multiconference (SpringSim’10), art. no. 213 (2010)Google Scholar
  99. 99.
    A. Nayfeh, D. Mook, Nonlinear Oscillations (Wiley-Interscience, New York, 1979)MATHGoogle Scholar
  100. 100.
    H. Olsson, K.J. Astrom, C. Canudas de Wit, M. Gaefvert, P. Lischinsky, Friction models and friction compensation. Eur. J. Control 4(3), 176–195 (1998)MATHGoogle Scholar
  101. 101.
    G.F. Oster, D.M. Auslander, Memristor: a new bond graph element. Trans. ASME Dyn. Syst. Meas. Contr. 94(3), 249–252 (1972)Google Scholar
  102. 102.
    B. Ould Bouamama, Bond graph approach as analysis tool in thermofluid model library conception. J. Franklin Inst. 340(1), 1–23 (2003)MathSciNetMATHCrossRefGoogle Scholar
  103. 103.
    B. Ould Bouamama, K. Medjaher, A.K. Samantaray, M. Staroswiecki, Supervision of an industrial steam generator. Part I: Bond graph modelling. Control Eng. Pract. 14(1), 71–83 (2005)CrossRefGoogle Scholar
  104. 104.
    D.A. Palmer, Modelling and control of suspensions as used in interferometric gravitational wave detectors. Ph.D. thesis, University of Glasgow, 2003Google Scholar
  105. 105.
    P.M. Pathak, A. Mukherjee, A. Dasgupta, Impedance control of space robots using passive degrees of freedom in controller domain. Trans. ASME: J. Dyn. Syst. Meas. Control 127(4), 564–578 (2005)CrossRefGoogle Scholar
  106. 106.
    H.M. Paynter, Analysis and design of Engineering Systems (M.I.T. Press, Cambridge, 1961)Google Scholar
  107. 107.
    E. Pedersen, Rotordynamics and bondgraphs: basic model. Math. Comput. Model. Dyn. Syst. 15(4), 337–352 (2009)MathSciNetCrossRefGoogle Scholar
  108. 108.
    H. Prahlad, I. Chopra, Comparative evaluation of shape memory alloy constitutive models with experimental data. J. Int. Mater. Syst. Struct. 12(6), 383–395 (2001)CrossRefGoogle Scholar
  109. 109.
    A. Preumont, Mechatronics: Dynamics of Electromechanical and Piezoelectric Systems (Springer, Heidelberg, 2006)Google Scholar
  110. 110.
    R.H. Rand, R.J. Kinsey, D.L. Mingori, Dynamics of spinup through resonance. Int. J. Non-Linear Mech. 27(3), 489–502 (1992)MATHCrossRefGoogle Scholar
  111. 111.
    J.E.B. Randles, Kinetics of rapid electrode reactions. Discuss. Faraday Soc. 1, 11 (1947)Google Scholar
  112. 112.
    J.N. Reddy, Nonlinear Finite Element Analysis (Oxford University Press, Oxford, 2007)Google Scholar
  113. 113.
    T.A. Rich, Thermo-mechanics of bimetal. Gen. Electr. Rev. 37(2), 102–105 (1934)Google Scholar
  114. 114.
    J.M. Rodriguez-Fortun, J. Orus, F. Buil, J.A. Castellanos, General bond graph model for piezoelectric actuators and methodology for experimental identification. Mechatronics 20, 303–314 (2010)CrossRefGoogle Scholar
  115. 115.
    G. Romero, J. Felez, J. Maroto, M.L. Martinez, Kinematic analysis of mechanism by using bond-graph language, in Proceedings 20th European Conference on Modelling and Simulation, 2006Google Scholar
  116. 116.
    G. Romero, J. Felez, J. Maroto, J.M. Mera, Efficient simulation of mechanism kinematics using bond graphs. Simul. Model. Pract. Theory 17, 293–308 (2009)CrossRefGoogle Scholar
  117. 117.
    B. Samanta, A. Mukherjee, Analysis of acoustoelastic systems using modal bond graphs. Trans. ASME J. Dyn. Syst. Meas. Control 112(1), 108–115 (1990)CrossRefGoogle Scholar
  118. 118.
    A.K. Samantaray, K. Medjaher, B. Ould Bouamama, M. Staroswiecki, G. Dauphin-Tanguy, Component based modelling of thermo-fluid systems for sensor placement and fault detection. SIMULATION: Trans. Soc. Model. Simul. Int. 80(7–8), 381–398 (2004)Google Scholar
  119. 119.
    A.K. Samantaray, B. Ould Bouamama, Model-based Process Supervision—A Bond Graph Approach (Springer, London, 2008)Google Scholar
  120. 120.
    A.K. Samantaray, A note on internal damping induced self-excited vibration in a rotor by considering source loading of a DC motor drive. Int. J. Non-Linear Mech. 43(9), 1012–1017 (2008)CrossRefGoogle Scholar
  121. 121.
    A.K. Samantaray, On the non-linear phenomena due to source loading in rotor-motor systems. Proc. IMechE Part-C: J. Mech. Eng. Sci. 223(4), 809–818 (2009)Google Scholar
  122. 122.
    A.K. Samantaray, Steady state dynamics of a non-ideal rotor with internal damping and gyroscopic effects. Nonlinear Dyn. 56(4), 443–451 (2009)MATHCrossRefGoogle Scholar
  123. 123.
    A.K. Samantaray, R. Bhattacharyya, A. Mukherjee, An investigation into the physics behind the stabilizing effects of two-phase lubricants in journal bearings. J. Vib. Control 12(4), 425–442 (2006)MATHCrossRefGoogle Scholar
  124. 124.
    A.K. Samantaray, R. Bhattacharyya, A. Mukherjee, On the stability of Crandall gyropendulum. Phys. Lett. A 372, 238–243 (2008)MATHCrossRefGoogle Scholar
  125. 125.
    A.K. Samantaray, S.S. Dasgupta, R. Bhattacharyya, Bond graph modeling of an internally damped nonideal flexible spinning shaft. J. Dyn. Syst. Meas. Control Trans. ASME 132(6), art. no. 061502 (2010)Google Scholar
  126. 126.
    A.K. Samantaray, S.S. Dasgupta, R. Bhattacharyya, Sommerfeld effect in rotationally symmetric planar dynamical systems. Int. J. Eng. Sci. 48(1), 21–36 (2010)CrossRefGoogle Scholar
  127. 127.
    A.K. Samantaray, A. Mukherjee, R. Bhattacharyya, Some studies on rotors with polynomial type non-linear external and internal damping. Int. J. Non-Linear Mech. 41(9), 1007–1015 (2006)MATHCrossRefGoogle Scholar
  128. 128.
    M. Schepers, Modeling a piezoelectric inertial stepping turntable using bond graphs. Master’s thesis, University of Twente, 2004Google Scholar
  129. 129.
    W. Schiehlen, Multibody Systems Handbook (Springer, Berlin, 1990)MATHCrossRefGoogle Scholar
  130. 130.
    D.J. Segalman, G.G. Parker, D.J. Inman, in Vibration Suppression by Modulation of Elastic Modulus Using Shape Memory Alloy. ed. by M. Shahinpoor, H.S. Tzou. Intelligent Structures, Materials and Vibration, vol. 58, pp. 1–5. ASME, 1993Google Scholar
  131. 131.
    A. Sommerfeld, Beitrge zum dynamischen ausbau der festigkeitslehe. Physikal Zeitschr 3, 266–286 (1902)MATHGoogle Scholar
  132. 132.
    J.S. Stecki, Bond graph modelling of power transmission by torque converting mechanisms. J. Franklin Inst. 311(2), 93–110 (1981)CrossRefGoogle Scholar
  133. 133.
    D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, The missing memristor found. Nature 453, 80–83 (2008)CrossRefGoogle Scholar
  134. 134.
    Y. Sugiyama, M.A. Langthjem, Physical mechanism of the destabilizing effect of damping in continuous non-conservative dissipative systems. Int. J. Non-Linear Mech. 42, 132–145 (2007)CrossRefGoogle Scholar
  135. 135.
    E. Suhir, Predictive analytical thermal stress modeling in electronics and photonics. Appl. Mech. Rev. 62, 040801 (2009)Google Scholar
  136. 136.
    K. Tanaka, A thermomechanical sketch of shape memory effect; one dimensional tensile behavior. Res. Mech. 18, 251–263 (1986)Google Scholar
  137. 137.
    J.U Thoma, B. Ould Bouamama, Modelling and Simulation in Thermal and Chemical Engineering. Bond Graph Approach (Springer, Telos, 2000)Google Scholar
  138. 138.
    W.T. Thomson, M.D. Dahleh, Theory of Vibration with Applications (Prentice Hall, Upper Saddle River, 1998)Google Scholar
  139. 139.
    Q. Tian, Y. Zhang, L. Chen, J. Yang, Simulation of planar flexible multibody systems with clearance and lubricated revolute joints. Nonlinear Dyn. 60, 489–511 (2010)MATHCrossRefGoogle Scholar
  140. 140.
    S. Timoshenko, Analysis of bi-metal thermostats. J. Opt. Soc. Am. 11(3), 233–255 (1925)CrossRefGoogle Scholar
  141. 141.
    S. Timoshenko, Vibration Problems in Engineering (Van Nostrand, Princeton, 1961)Google Scholar
  142. 142.
    S.T. Todd, A. Jain, H. Xie, A multi-degree-of-freedom micromirror utilizing inverted-series-connected bimorph actuators. J. Opt. A: Pure Appl. Opt. 8, S352–S359 (2006)CrossRefGoogle Scholar
  143. 143.
    S.T. Todd, Electrothermomechanical modeling of a 1-D electrothermal MEMS micromirror. Master’s thesis, University of Florida, 2005Google Scholar
  144. 144.
    A. Tonoli, N. Amati, Dynamic modeling and experimental validation of eddy current dampers and couplers. J. Vib. Acoust. 130 article no. 021011, 1–9 (2008)Google Scholar
  145. 145.
    N. Vahdati, S. Heidari, Bond graph model of a multi-layer piezoelectric (pzt) beam and its application in semi-active hydraulic mounts, in ASME 2009 Dynamic Systems and Control Conference (DSCC2009), Paper no. DSCC2009-2786, pp. 347–354, Hollywood, California, USA, 12–14 October 2009Google Scholar
  146. 146.
    Z. Viderman, I. Porat, An optimal-control method for passage of a flexible rotor through resonances. Trans. ASME J. Dyn. Syst. Meas. Control 109(3), 216–223 (1987)MATHCrossRefGoogle Scholar
  147. 147.
    D. Vischer, H. Bleuler, Self-sensing active magnetic levitation. IEEE Trans. Magn. 29(2), 1276–1281 (1993)CrossRefGoogle Scholar
  148. 148.
    W. Wang, D. Shin, C. Han, H. Choi, Modeling and simulation for dual stage system using bond graph theory, in ISOT 2009—International Symposium on Optomechatronic Technologies, art. no. 5326087, pp. 197–202, 2009Google Scholar
  149. 149.
    T.M. Wasfy, A.K. Noor, Computational strategies for flexible multibody systems. Appl. Mech. Rev. 56(6), 553–613 (2003)Google Scholar
  150. 150.
    M. Wassink, R. Carloni, S. Stramigioli, Port-hamiltonian analysis of a novel robotic finger concept for minimal actuation variable impedance grasping, in Proceedings—IEEE International Conference on Robotics and Automation, number art. 5509871, 771–776 (2010)Google Scholar
  151. 151.
    J. Wauer, S. Suherman, Vibration suppression of rotating shafts passing through resonances by switching shaft stiffness. J. Vib. Acoust. 120, 170–180 (1997)CrossRefGoogle Scholar
  152. 152.
    Y. Xing, E. Pedersen, T. Moan, An inertia-capacitance beam substructure formulation based on the bond graph method with application to rotating beams. J. Sound Vib. 330(21), 5114–5130 (2011)CrossRefGoogle Scholar
  153. 153.
    T.-J. Yeh, Y.-J. Chung, W.-C. Wu, Sliding control of magnetic bearing systems. J. Dyn. Syst. Meas. Control 123, 353–362 (2001)Google Scholar
  154. 154.
    T.-J. Yeh, H. Ruo-Feng, L. Shin-Wen, An integrated physical model that characterizes creep and hysteresis in piezoelectric actuators. Simul. Model. Pract. Theory 16(1), 93–110 (2008)CrossRefGoogle Scholar
  155. 155.
    A.J. Zak, M.P. Cartmell, W.M. Ostachowicz, Dynamics and control of a rotor using and integrated SMA/composite active bearing actuator, in 5th International Conference on Damage Assessment of Structures, pp. 233–240, University of Southampton, UK, 2003Google Scholar
  156. 156.
    W. Zaki, Z. Moumni, A three-dimensional model of the thermomechanical behavior of shape memory alloys. J. Mech. Phys. Solids 55, 2455–2490 (2007)MATHCrossRefGoogle Scholar
  157. 157.
    A. Zeid, C.H. Chung, Bond graph modeling of multibody systems: a library of three-dimensional joints. J. Franklin Inst. 329(4), 605–636 (1992)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Rochdi Merzouki
    • 1
  • Arun Kumar Samantaray
    • 2
  • Pushparaj Mani Pathak
    • 3
  • Belkacem Ould Bouamama
    • 1
  1. 1.Technologies de Lille (USTL), Ecole Polytechnique de LilleUniversité des Sciences etVilleneuve D’Ascq CXFrance
  2. 2.Department of Mechanical EngineeringIndian Institute of TechnologyKharagpurIndia
  3. 3.Department of Mechanical and Industrial EngineeringIndian Institute of TechnologyRoorkeeIndia

Personalised recommendations