M.Sc Thesis

M.Sc StudentBen Farkash
SubjectSwitching between buckling modes using dynamic excitation
DepartmentDepartment of Mechanical Engineering
Supervisors Full Professors Bucher Izhak
Dr. Gabay Ran
Dr. Plat Harel
Full Thesis textFull thesis text - English Version


This thesis is concerned with dynamical systems capable of producing motion in several degrees of freedom using a single actuator. The research focuses on a two degrees of freedom system capable of moving between nonlinear buckling states in a continuous manner such that its motion resembles a traveling wave. The motivation to this research was initiated by miniature swimming and flying robots and by applications were traveling waves are needed. In order to propel itself in a viscous environment, a miniature swimmer must have different swimming sequence than the conventional ones. Reciprocal motions will be inefficient and a better strategy will constitute of a sequence of spatial configuration in the form of a traveling wave. In this work it will be shown how such a movement can be achieved. A two degrees of freedom mechanism was chosen in order to allow for relatively large amplitudes. The mechanism has two stable symmetric buckling modes and two unstable symmetric buckling modes, which create two stable potential wells and two unstable saddle points, respectively in the three dimensional potential map surface. Drawing a trajectory on the potential surface which passes through the four different buckling points, one achieves a spatial displacements sequence of the mechanism resembling a traveling wave. The potential surface geometry is controlled by the system’s buckling preload which enables larger amplitudes and deeper wells when increased. A model for such a system is created and investigated using Lagrange equations. The model’s dynamical properties are investigated including local linearization at the system stable points. The local natural frequencies and mode shapes are computed, and those lead to a suitable choice of dynamic excitation (force and parametric resonance) in order to create the continuous motion on the potential map. It was found that an excitation at a local resonance is an efficient way to achieve large amplitudes using relatively low levels of power which is useful for the case of power limited miniature swimmers. The model is followed by a description of an experimental rig which represents the above model. The experimental rig’s static and dynamical properties are explored through a series of experiments revealing the system’s stable points, natural frequencies and damping coefficients. The model is then updated with the fitted experimental parameters and compared to the experimental results, showing a reasonable agreement. Finally, a series of experiments is shown revealing a periodic trajectory exhibited by a closed curve on the potential surface which creates a planar motion resembling a traveling wave