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Biomimetic flexible plate actuators are faster and more efficient with a passive attachment

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Abstract

Using three-dimensional computer simulations, we probe biomimetic free swimming of an internally actuated flexible plate in the regime near the first natural frequency. The plate is driven by an oscillating internal moment approximating the actuation mechanism of a piezoelectric macro fiber composite (MFC) bimorph. We show in our simulations that the addition of a passive attachment increases both swimming velocity and efficiency. Specifically, if the active and passive sections are of similar size, the overall performance is the best. We determine that this optimum is a result of two competing factors. If the passive section is too large, then the actuated portion is unable to generate substantial deflection to create sufficient thrust. On the other hand, a large actuated section leads to a bending pattern that is inefficient at generating thrust especially at higher frequencies.

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References

  1. Sfakiotakis, M., Lane, D.M., Davies, J.B.C.: Review of fish swimming modes for aquatic locomotion. IEEE J. Ocean. Eng. 24, 237–252 (1999)

    Article  Google Scholar 

  2. Flammang, B., Lauder, G.: Caudal fin shape modulation and control during acceleration, braking and backing maneuvers in bluegill sunfish, Lepomis macrochirus. J. Exp. Biol. 212, 277–286 (2009)

    Article  Google Scholar 

  3. Esposito, C.J., Tangorra, J.L., Flammang, B.E., et al.: A robotic fish caudal fin: effects of stiffness and motor program on locomotor performance. J. Exp. Biol. 215, 56–67 (2012)

  4. Flammang, B.E., Lauder, G.V.: Speed-dependent intrinsic caudal fin muscle recruitment during steady swimming in bluegill sunfish, Lepomis macrochirus. J. Exp. Biol. 211, 587–598 (2008)

    Article  Google Scholar 

  5. Lauder, G.V., Tangorra, J.L.: Fish Locomotion: Biology and Robotics of Body and Fin-based Movements. In: Robot Fish, 25–49. Springer, New York (2015)

  6. Barrett, D.S.: Propulsive efficiency of a flexible hull underwater vehicle. [Ph.D. Thesis], Massachusetts Institute of Technology, Boston (1996)

  7. Anderson, J.M., Chhabra, N.K.: Maneuvering and stability performance of a robotic tuna. Integr. Comp. Biol. 42, 118–126 (2002)

    Article  Google Scholar 

  8. Hirata, K.: Development of experimental fish robot. In: Sixth International Symposium on Marine Engineering 2000, 235–240

  9. Ding, R., Yu, J., Yang, Q., et al.: CPG-based dynamics modeling and simulation for a biomimetic amphibious robot. In: 2009 IEEE International Conference on Robotics and Biomimetics (ROBIO), 1657–1662. IEEE (2009)

  10. Liu, F., Lee, K.M., Yang, C.J.: Hydrodynamics of an undulating fin for a wave-like locomotion system design. IEEE/ASME Trans. Mechatron. 17, 554–562 (2012)

    Article  Google Scholar 

  11. Kopman, V., Laut, J., Acquaviva, F., et al.: Dynamic modeling of a robotic fish propelled by a compliant tail. IEEE J. Ocean. Eng. 40, 209–221 (2015)

  12. Shahinpoor, M.: Conceptual design, kinematics and dynamics of swimming robotic structures using ionic polymeric gel muscles. Smart Mater. Struct. 1, 91–95 (1992)

    Article  Google Scholar 

  13. Mojarrad, M., Shahinpoor, M.: Noiseless propulsion for swimming robotic structures using polyelectrolyte ion-exchange membrane. Proc. SPIE 2716, 183–192 (1996)

    Article  Google Scholar 

  14. Chen, Z., Um, T.I., Zhu, J.: Bio-inspired robotic cownose ray propelled by electroactive polymer pectoral fin. In: ASME 2011 International Mechanical Engineering Congress and Exposition, 1–8 (2011)

  15. Chen, Z., Um, T.I., Bart-Smith, H.: Ionic polymer–metal composite enabled robotic manta ray. Proc. SPIE 7976, 797637 (2011)

    Article  Google Scholar 

  16. Chen, Z., Shatara, S., Tan, X.B.: Modeling of biomimetic robotic fish propelled by an ionic polymer–metal composite caudal fin. IEEE/ASME Trans. Mechatron. 15, 448–459 (2010)

    Article  Google Scholar 

  17. Aureli, M., Kopman, V., Porfiri, M.: Free-locomotion of underwater vehicles actuated by ionic polymer metal composites. IEEE/ASME Trans. Mechatron. 15, 603–614 (2010)

    Article  Google Scholar 

  18. Shen, Q., Wang, T., Kim, K.J.: A biomimetic underwater vehicle actuated by waves with ionic polymer–metal composite soft sensors. Bioinspir. Biomim. 10, 055007 (2015)

    Article  Google Scholar 

  19. Cho, K.J., Hawkes, E., Quinn, C., et al.: Design, fabrication and analysis of a body-caudal fin propulsion system for a microrobotic fish. In: 2008 IEEE International Conference on Robotics and Automation, 706–711 (2008)

  20. Wang, Z.L., Hang, G.R., Li, J.A., et al.: A micro-robot fish with embedded SMA wire actuated flexible biomimetic fin. Sens. Actuators A 144, 354–360 (2008)

  21. Shinjo, N., Swain, G.W.: Use of a shape memory alloy for the design of an oscillatory propulsion system. IEEE J. Ocean. Eng. 29, 750–755 (2004)

    Article  Google Scholar 

  22. Wang, Z., Hang, G., Wang, Y., et al.: Embedded SMA wire actuated biomimetic fin: a module for biomimetic underwater propulsion. Smart Mater. Struct. 17, 025039 (2008)

  23. Rossi, C., Colorado, J., Coral, W., et al.: Bending continuous structures with SMAs: a novel robotic fish design. Bioinspir. Biomim. 6, 045005 (2011)

  24. Rossi, C., Coral, W., Colorado, J., et al.: A motor-less and gear-less bio-mimetic robotic fish design. In: 2011 IEEE International Conference on Robotics and Automation, 3646–3651 (2011)

  25. Zhang, Y.S., Liu, G.J.: Design, analysis and experiments of a wireless swimming micro robot. In: 2005 IEEE International Conference on Mechatronics and Automations, 946–951 (2005)

  26. Zhang, Y.S., Liu, G.J.: Wireless micro biomimetic swimming robot based on giant magnetostrictive films. In: 2005 IEEE International Conference on Robotics and Biomimetics, 195–200 (2006)

  27. Zhang, Y.S., Liu, G.J.: Wireless swimming microrobot: design, analysis, and experiments. J. Dyn. Syst. Meas. Control 131, 011004 (2009)

    Article  Google Scholar 

  28. Zhang, Z., Philen, M., Neu, W.: A biologically inspired artificial fish using flexible matrix composite actuators: analysis and experiment. Smart Mater. Struct. 19, 094017 (2010)

    Article  Google Scholar 

  29. Zhang, Z.G.: Design and control of a fish-like robot using an electrostatic motor. In: 2007 IEEE International Conference on Robotics and Automation, 974–979 (2007)

  30. Philen, M., Neu, W.: Hydrodynamic analysis, performance assessment, and actuator design of a flexible tail propulsor in an artificial alligator. Smart Mater. Struct. 20, 094015 (2011)

    Article  Google Scholar 

  31. Erturk, A., Inman, D.J.: Piezoelectric Energy Harvesting. Wiley, New York (2011)

    Book  Google Scholar 

  32. Fukuda, T., Kawamoto, A., Arai, F., et al.: Steering mechanism and swimming experiment of micro mobile robot in water. In: IEEE Proceedings, Micro Electro Mechanical Systems, 300–305 (1995)

  33. Wiguna, T., Heo, S., Park, H.C., et al.: Design and experimental parametric study of a fish robot actuated by piezoelectric actuators. J. Intell. Mater. Syst. Struct. 20, 751–758 (2009)

  34. Heo, S., Wiguna, T., Park, H.C., et al.: Effect of an artificial caudal fin on the performance of a biomimetic fish robot propelled by piezoelectric actuators. J. Bionic Eng. 4, 151–158 (2007)

  35. Ming, A.G., Park, S., Nagata, Y., et al.: Development of underwater robots using piezoelectric fiber composite. In: 2009 IEEE International Conference on Robotics and Automation, 3435–3440 (2009)

  36. Wilkie, W.K., Bryant, R.G., High, J.H., et al.: Low-cost piezocomposite actuator for structural control applications. Proc. SPIE 3991, 323–334 (2000)

  37. High, J.W., Wilkie, W.K.: Method of Fabricating NASA-Standard Macro-fiber Composite Piezoelectric Actuators. National Aeronautics and Space Administration, Langley Research Center, Hampton (2003)

    Google Scholar 

  38. Bryant, R.G.: Overview of NASA Langley’s Piezoelectric Ceramic Packaging Technology and Applications. National Aeronautics and Space Administration, Langley Research Center, Hampton (2007)

    Google Scholar 

  39. Cen, L., Erturk, A.: Bio-inspired aquatic robotics by untethered piezohydroelastic actuation. Bioinspir. Biomim. 8, 016006 (2013)

    Article  Google Scholar 

  40. Erturk, A., Inman, D.J.: An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart Mater. Struct. 18, 025009 (2009)

    Article  Google Scholar 

  41. Erturk, A., Delporte, G.: Underwater thrust and power generation using flexible piezoelectric composites: an experimental investigation toward self-powered swimmer-sensor platforms. Smart Mater. Struct. 20, 125013 (2011)

    Article  Google Scholar 

  42. Zhang, J., Liu, N.S., Lu, X.Y.: Locomotion of a passively flapping flat plate. J. Fluid Mech. 659, 43–68 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  43. Hua, R.-N., Zhu, L., Lu, X.-Y.: Locomotion of a flapping flexible plate. Phys. Fluids 25, 121901 (2013)

    Article  Google Scholar 

  44. de Sousa, P.J.S.A.F., Allen, J.J.: Thrust efficiency of harmonically oscillating flexible flat plates. J. Fluid Mech. 674, 43–66 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  45. Li, G.J., Zhu, L.D., Lu, X.Y.: Numerical studies on locomotion performance of fish-like tail fins. J. Hydrodyn. 24, 488–495 (2012)

    Article  Google Scholar 

  46. Huang, W.-X., Shin, S.J., Sung, H.J.: Simulation of flexible filaments in a uniform flow by the immersed boundary method. J. Comput. Phys. 226, 2206–2228 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  47. Lee, J.H., Huang, W.-X., Sung, H.J.: Flapping dynamics of a flexible flag in a uniform flow. Fluid Dyn. Res. 46, 055517 (2014)

    Article  Google Scholar 

  48. Facci, A.L., Porfiri, M.: Analysis of three-dimensional effects in oscillating cantilevers immersed in viscous fluids. J. Fluid. Struct. 38, 205–222 (2013)

    Article  Google Scholar 

  49. Huang, W.-X., Chang, C.B., Sung, H.J.: An improved penalty immersed boundary method for fluid–flexible body interaction. J. Comput. Phys. 230, 5061–5079 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  50. Engels, T., Kolomenskiy, D., Schneider, K., et al.: Numerical simulation of fluid–structure interaction with the volume penalization method. J. Comput. Phys. 281, 96–115 (2015)

  51. Li, G.-J., Liu, N.-S., Lu, X.-Y.: Dynamic performance and wake structure of flapping plates with different shapes. Acta Mech. Sin. 30, 800–808 (2014)

  52. Yeh, P.D., Alexeev, A.: Effect of aspect ratio in free-swimming plunging flexible plates. Comput. Fluids 124, 220–225 (2016)

    Article  MathSciNet  Google Scholar 

  53. Yeh, P.D., Alexeev, A.: Free swimming of an elastic plate plunging at low Reynolds number. Phys. Fluids 26, 053604 (2014)

    Article  Google Scholar 

  54. Dai, H., Luo, H.X., de Sousa, P.J.S.A.F., et al.: Thrust performance of a flexible low-aspect-ratio pitching plate. Phys. Fluids 24, 101903 (2012)

  55. Huang, W.-X., Sung, H.J.: Three-dimensional simulation of a flapping flag in a uniform flow. J. Fluid Mech. 653, 301–336 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  56. Moored, K., Dewey, P., Boschitsch, B., et al.: Linear instability mechanisms leading to optimally efficient locomotion with flexible propulsors. Phys. Fluids 26, 041905 (2014)

  57. Quinn, D.B., Lauder, G.V., Smits, A.J.: Maximizing the efficiency of a flexible propulsor using experimental optimization. J. Fluid Mech. 767, 430–448 (2015)

    Article  Google Scholar 

  58. Dewey, P.A., Boschitsch, B.M., Moored, K.W., et al.: Scaling laws for the thrust production of flexible pitching panels. J. Fluid Mech. 732, 29–46 (2013)

  59. Quinn, D.B., Lauder, G.V., Smits, A.J.: Scaling the propulsive performance of heaving flexible panels. J. Fluid Mech. 738, 250–267 (2014)

    Article  Google Scholar 

  60. Alben, S., Witt, C., Baker, T.V., et al.: Dynamics of freely swimming flexible foils. Phys. Fluids 24, 051901 (2012)

  61. Piñeirua, M., Godoy-Diana, R., Thiria, B.: Resistive thrust production can be as crucial as added mass mechanisms for inertial undulatory swimmers. Phys. Rev. E 92, 021001 (2015)

    Article  Google Scholar 

  62. Marais, C., Thiria, B., Wesfreid, J.E., et al.: Stabilizing effect of flexibility in the wake of a flapping foil. J. Fluid Mech. 710, 659–669 (2012)

  63. Raspa, V., Ramananarivo, S., Thiria, B., et al.: Vortex-induced drag and the role of aspect ratio in undulatory swimmers. Phys. Fluids 26, 041701 (2014)

  64. Shelley, M.J., Zhang, J.: Flapping and bending bodies interacting with fluid flows. Annu. Rev. Fluid Mech. 43, 449–465 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  65. Ladd, A.J.C., Verberg, R.: Lattice-Boltzmann simulations of particle-fluid suspensions. J. Stat. Phys. 104, 1191–1251 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  66. Ostoja-Starzewski, M.: Lattice models in micromechanics. Appl. Mech. Rev. 55, 35–60 (2002)

    Article  MATH  Google Scholar 

  67. Buxton, G.A., Verberg, R., Jasnow, D., et al.: Newtonian fluid meets an elastic solid: coupling lattice Boltzmann and lattice-spring models. Phys. Rev. E 71, 056707 (2005)

  68. Mao, W.: Modeling particle suspensions using lattice Boltzmann method. [Ph.D. Thesis], Georgia Institute of Technology, Atlanta, USA (2013)

  69. Verlet, L.: Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 159, 98–103 (1967)

    Article  Google Scholar 

  70. Verlet, L.: Computer “experiments” on classical fluids. II. Equilibrium correlation functions. Phys. Rev. 165, 201–214 (1968)

    Article  Google Scholar 

  71. Chen, H., Filippova, O., Hoch, J., et al.: Grid refinement in lattice Boltzmann methods based on volumetric formulation. Physica A 362, 158–167 (2006)

  72. Mills, Z.G., Aziz, B., Alexeev, A.: Beating synthetic cilia enhance heat transport in microfluidic channels. Soft Matter 8, 11508–11513 (2012)

    Article  Google Scholar 

  73. Masoud, H., Bingham, B.I., Alexeev, A.: Designing maneuverable micro-swimmers actuated by responsive gel. Soft Matter 8, 8944–8951 (2012)

    Article  Google Scholar 

  74. Alexeev, A., Balazs, A.C.: Designing smart systems to selectively entrap and burst microcapsules. Soft Matter 3, 1500–1505 (2007)

    Article  Google Scholar 

  75. Ballard, M., Mills, Z.G., Beckworth, S., et al.: Enhancing nanoparticle deposition using actuated synthetic cilia. Microfluid. Nanofluid. 17, 317–324 (2014)

  76. Alexeev, A., Verberg, R., Balazs, A.C.: Modeling the motion of microcapsules on compliant polymeric surfaces. Macromolecules 38, 10244–10260 (2005)

    Article  Google Scholar 

  77. Masoud, H., Alexeev, A.: Resonance of flexible flapping wings at low Reynolds number. Phys. Rev. E 81, 056304 (2010)

    Article  Google Scholar 

  78. Mao, W., Alexeev, A.: Hydrodynamic sorting of microparticles by size in ridged microchannels. Phys. Fluids 23, 051704 (2011)

    Article  Google Scholar 

  79. Mao, W.B., Alexeev, A.: Motion of spheroid particles in shear flow with inertia. J. Fluid Mech. 749, 145–166 (2014)

    Article  Google Scholar 

  80. Kilimnik, A., Mao, W., Alexeev, A.: Inertial migration of deformable capsules in channel flow. Phys. Fluids 23, 123302 (2011)

  81. Bouzidi, M., Firdaouss, M., Lallemand, P.: Momentum transfer of a Boltzmann-lattice fluid with boundaries. Phys. Fluids 13, 3452–3459 (2001)

    Article  MATH  Google Scholar 

  82. Van Eysden, C.A., Sader, J.E.: Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope: arbitrary mode order. J. Appl. Phys. 101, 044908 (2007)

    Article  Google Scholar 

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Acknowledgments

The authors would like to thank L. Cen and A. Erturk for the stimulating and insightful discussions.

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Yeh, P.D., Alexeev, A. Biomimetic flexible plate actuators are faster and more efficient with a passive attachment. Acta Mech. Sin. 32, 1001–1011 (2016). https://doi.org/10.1007/s10409-016-0592-0

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  • DOI: https://doi.org/10.1007/s10409-016-0592-0

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