Author's School

School of Engineering & Applied Science

Author's Department/Program

Mechanical Engineering and Materials Science


English (en)

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)

Chair and Committee

David Peters


Sinusoidal locomotion is commonly seen in snakes, fish, nematodes, or even the wings of some birds and insects. This doctoral thesis presents the study of sinusoidal locomotion of the nematode C. elegansin experiments and the application of the state-space airloads theory to the theoretical forces of sinusoidal motion. An original MATLAB program has been developed to analyze the video records of C. elegans' movement in different fluids, including Newtonian and non-Newtonian fluids. The experimental and numerical studies of swimming C. elegans has revealed three conclusions. First, though the amplitude and wavelength are varying with time, the motion of swimming C. elegans can still be viewed as sinusoidal locomotion with slips. The average normalized wavelength is a conserved character of the locomotion for both Newtonian and non-Newtonian fluids. Second, fluid viscosity affects the frequency but not the moving speed of C. elegans, while fluid elasticity affects the moving speed but not the frequency. Third, by the resistive force theory, for more elastic fluids the ratio of resistive coefficients becomes smaller. Inspired by the motion of C. elegans and other animals performing sinusoidal motion, we investigated the sinusoidal motion of a thin flexible wing in theory. Given the equation of the motion, we have derived the closed forms of propulsive force, lift and other generalized forces applying on the wing. We also calculated the power required to perform the motion, the power lost due to the shed vortices and the propulsive efficiency. These forces and powers are given as functions of reduced frequency k, dimensionless wavelength z, dimensionless amplitude A/b, and time. Our results show that a positive, time-averaged propulsive force is produced for all k>k0=&pi/z. At k=k0, which implies the moment when the moving speed of the wing is the same as the wave speed of its undulation, the motion reaches a steady state with all forces being zero. If there were no shed vorticity effects, the propulsive force would be zero at z = 0.569 and z = 1.3 for all k, and for a fixed k the wing would gain the optimal propulsive force when z = 0.82. With the effects of shed vorticity, the propulsive efficiency decreases from 1.0 to 0.5 as k goes to infinity, and the propulsive efficiency increases almost in a linear relationship with k0.



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