@Article{icces.2023.09812,
AUTHOR = {Mengfan Xu, Yongliang Yu},
TITLE = {The Body Deformation and Energy Transfer of Undulatory Propulsion in  Fish Swimming},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {25},
YEAR = {2023},
NUMBER = {1},
PAGES = {1--2},
URL = {http://www.techscience.com/icces/v25n1/53782},
ISSN = {1933-2815},
ABSTRACT = {During the steady swimming of carangiform or anguilliform swimmers, the fish body shows significant 
fluctuation characteristics. The formation of waving body is not only related to the driving force of fish 
muscle, but also to the material properties of fish body and fluid forces. In fluid mechanics, the propulsive 
force of fish body is closely related to reverse Kármán vortex street. However, there is still a lack of 
comprehensive understanding of the work done by the driving force, the formation of the fluctuation and 
propulsion of the fish. Based on the kinematic chain integration framework, the deformation of the fish body 
under the action of active bending moment is studied through theoretical analysis and numerical simulation, 
and the effect of the different component of fluid forces is analyzed. The study covers the discussion about 
wave propagation in both elastic bodies and fluid media, and re-examines the physical phenomenon of fish 
body deformation from the perspective of wave propagation.<br/>
The fish body is modelled as a freely supported Euler-Bernoulli beam, then the deformation of the beam and 
the energy transport under the active bending moment excitation are investigated. Furthermore, we discuss 
the approximation degree of the fluid force to the quadratic force model after removing the added mass 
term. In detail, the beam undergoes active and passive deformation due to the combined action of fluid 
forces and an active bending moment that is transmitted from the head to the tail as a right-hand traveling 
wave, and finally the forward propulsion is realized with the characteristic wake structure of the flow field. 
When the fluid action is absent, the bending wave that propagates in the beam reflects completely at both 
free ends of the beam, causing the deformation of the Euler-Bernoulli beam to exhibit standing wave 
characteristics and the center of mass of the beam to remain stationary. When the fluid action is considered, 
the right-traveling bending wave that occurs on the beam does not undergo complete reflection at the tail 
end, causing the beam to display a deformation of right-traveling wave and the beam to move to the left 
under the action of fluid force, leaving behind a wake structure of counter-Kármán vortices in the flow field. 
In general, the fluid forces acting on the undulatory beam can be decomposed into the added mass force and 
the resistive force, that are proposed by Lighthill and Taylor respectively. The present result shows that the 
resistive component corresponds to the vortex structure and the integral effect of the added mass term is 
zero in the steady swimming. In this process, the bending wave on the beam transfers the energy from front 
to anterior and transfers it into the flow field at the tail. Of course, there is a small amplitude wave is reflected 
from the tail end and superposed with the original right traveling bending wave, which makes the fish body 
still have a weak standing wave form although the travelling wave is the dominant feature in deformation. 
Thus, the undulatory propulsion of the fish body is an inevitable result of active excitation of the distributed 
muscles and the coupling between the fluid and the fish body. Energy is transferred to the fluid through the 
fish tail to generate thrust, and a reverse Kármán vortex street is formed in the flow field, which correspond 
to the undulatory propulsion.},
DOI = {10.32604/icces.2023.09812}
}