Abstract
This paper presents a Differential Quadrature Element Method for free transverse vibration of a robotic fish based on a continuous and non-uniform flexible backbone with distributed masses (fish ribs). The proposed method is based on the theory of a Timoshenko cantilever beam. The effects of the masses (number, magnitude and position) on the value of natural frequencies are investigated. Governing equations, compatibility and boundary conditions are formulated according to the Differential Quadrature rules. The convergence, efficiency and accuracy are compared to other analytical solution proposed in the literature. Moreover, the proposed method has been validate against the physical prototype of a flexible fish backbone. The main advantages of this method, compared to the exact solutions available in the literature are twofold: first, smaller computational cost and second, it allows analysing the free vibration in beams whose section is an arbitrary function, which is normally difficult or even impossible with other analytical methods.
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C.W. Bert, M. Malik, Appl. Mech. Rev. 49, 1 (1996)
Y. Cha, M. Verotti, H. Walcott, S. Peterson, M. Porfiri, Bioinspir. Biomimet. 8, 3 (2013)
Y. Chen, J. Appl. Mech. 30, 310 (1963)
W. Coral, et al., Smart Actuation and Sensing Systems – Recent Advances and Future Challenges. Chapter 3, SMA-Based Muscle-Like Actuation in Biologically Inspired Robots: A State of the Art Review (INTECH, 2012), p. 53
M.A. De Rosa, C. Franciosi, M.J. Maurizi, Comp. Struct. 58, 1145 (1955)
H. Du, M.K. Lim, N.R. Lin, Inter. J. Numer. Meth. Eng. 37, 1881 (1994)
H. Du, M.K. Lim, N.R. Lin, J. Sound Vibr. 181, 279 (1995)
M. Gurgoze, J. Sound Vibr. 96, 461 (1984)
M. Gurgoze, J. Sound Vibr. 100, 588 (1985)
T. Kaneko, J. Phys. D: Appl. Phys. 8, 1928 (1975)
G. Karami, P. Malekzadeh, Comp. Meth. Appl. Mech. Eng. 191, 3509 (2002)
P. Laura, M.J. Maurizi, J.L. Pombo, J. Sound Vibr. 41, 397 (1975)
P. Laura, P.L. Verniere de Irassar, G.M. Ficcadenti, J. Sound Vibr. 86, 279 (1983)
S.Y. Lee, S.M. Lin, J. Sound Vibr. 183, 403 (1995)
R.M. Lin, M.K. Lim, H. Du, Comput. Struct. 53, 993 (1994)
W.H. Liu, J.R. Wu, C.C. Huang, J. Sound Vibr. 122, 193 (1988)
G.V. Rao, K.M. Saheb, G.R. Janardhan, J. Sound Vibr. 298, 221 (2006)
C. Rossi, W. Coral, et al., Bioinspir. Biomimet. 6, 15 (2011)
C. Rossi, W. Coral, et al., A Motor-less and Gear-less Bio-mimetic Robotic Fish Design, 2011 IEEE International Conference on Robotics and Automation (2011)
S. Timoshenko, D.H. Young, W. Weaver, Vibration problems in engineering (Wiley, New York, 1974)
M. Aureli, V. Kopman, M. Porfiri, Free-locomotion of underwater vehicles actuated by ionic polymer metal composites. IEEE/ASME Transactions on 15(4), 603 (2010)
P. Phamduy, R. LeGrand, M. Porfiri, Robotics & Automation Magazine, IEEE 22(1), 86 (2015)
Tracker, Video Analysis and Modelling Tool, http://physlets.org/tracker/ (accessed September 10, 2015)
W.-H. Chu, Technical Report No. 2, DTMB, Contract NObs-86396(X), Southwest Research Institute (San Antonio, Texas, 1963)
U.S. Lindholm, D.D. Kana, W.-H. Chu, H.N. Abramson, J. Ship. Res. 9, 11 (1965)
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Coral, W., Rossi, C. & Curet, O. Free vibration analysis of a robotic fish based on a continuous and non-uniform flexible backbone with distributed masses. Eur. Phys. J. Spec. Top. 224, 3379–3392 (2015). https://doi.org/10.1140/epjst/e2015-50021-3
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DOI: https://doi.org/10.1140/epjst/e2015-50021-3