https://doi.org/10.1140/epjst/e2015-50021-3
Regular Article
Free vibration analysis of a robotic fish based on a continuous and non-uniform flexible backbone with distributed masses
1 Universidad Politécnica de Madrid, Madrid, Spain
2 Centre for Automation and Robotics (CAR) UPM-CSIC, Madrid, Spain
3 Department of Ocean and Mechanical Engineering, Florida Atlantic University (FAU), Boca Raton, USA
a e-mail: william.coral@gmail.com
Received: 7 March 2015
Revised: 2 November 2015
Published online: 15 December 2015
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.
© EDP Sciences, Springer-Verlag, 2015
