Ph.D Thesis

Ph.D StudentEyal Setter
SubjectTraveling Waves in Elastic Structures with Application to
DepartmentDepartment of Mechanical Engineering
Supervisor Full Professors Bucher Izhak
Full Thesis textFull thesis text - English Version


Traveling elastic waves force material points to oscillate along their path. The spatial motion of the material points can thus be exploited as a transport mechanism for either object translation and rotation, or self-propulsion in fluids under low Reynolds number environments.

This thesis describes a method to create unique flexural wave patterns in a vibrating structure. The method involves a force-tuning stage, through which dozens of external forcing elements’ outputs are modified automatically until the response, measured at hundreds of sensed locations, complies with the anticipated response. In an optimization stage, the best dynamic force vector that generates pre-specified deformation patterns is found. Among the obtainable periodic responses are standing or traveling flexural waves of single or multi-frequencies, in one to three spatial dimensions, as well as rotating, vortex-like flexural waves in 2D. The precise iterative tuning process can overcome mild nonlinearities by injecting forces that nullify their effect. The proposed tuning method showed good results in numerical simulations and in real world experiments.

Indeed, traveling waves are a common motility mechanism in low Reynolds numbers, in nature, and recently in micro-robotic applications. The swimming mechanism examined in this research is based on transverse, axisymmetric, surface traveling waves along a cylindrical long shell. An analytical solution is derived for waves of small amplitudes compared with the wavelength, underlining the effects of the wavelength, wave velocity, wave amplitude and wall thickness. Comparison with other swimming configurations such as planar or spatial waving tails showed that the proposed configuration is superior in hydrodynamic effectiveness as the ratio of the radius over wavelength increases. The theoretical model was extended to account for multiple traveling waves of arbitrary wavelengths, amplitudes and wave velocities, in the case of negligible wall thickness.

The analytical results were validated using numerical simulations (ComsolTM) and experiments, in which a (macro) robotic swimmer was set in highly viscous silicon fluid, and self-propelled by transverse surface traveling waves, generated by a unique mechanical mechanism. The swimmer velocity was recorded using image processing techniques. The actual experimental wave profile, however, is not a pure sine and is composed of several spatial harmonics. A novel method is developed to experimentally detect and decompose a given time-dependent waveform into its components. Doing so, the phase, amplitude and wavelength of each component in the deforming surface can be estimated by means of time-space least squares. The experimental results fit well the modified analytical predictions, accounting for added passive drag.