Ph.D Thesis

Ph.D StudentRan Gabai
SubjectGenerating, Sensing and Controlling Progressive Waves in One
and Two Dimensions, a Theoretical and Experimental
DepartmentDepartment of Mechanical Engineering
Supervisor Full Professors Bucher Izhak
Full Thesis textFull thesis text - English Version


This research discusses several aspects of structural vibrations using a traveling waves perspective. The purpose of this work is to develop the understanding, theoretical methodology and, tools to create traveling waves in structures. Traveling wave vibrations are desired in variety of engineering fields for the purpose of propulsion, energy conveying, suppression of noise and vibrations, and in closed loop control of flexible structures.

Since a vibrating structure rarely lends itself to vibrate in a traveling wave pattern, it is necessary to apply special excitation methods in order to generate such a response. This research puts some emphasize on finding analytically the optimal excitation in order to generate a pure progressive wave in a structure. A new analytical development that uses structural analysis tools to calculate the spatial excitation distribution is presented. This analytical approach is further expanded to a numerical implementation on discrete systems that finds the required locations of discrete actuators yielding a particular response.

The effect of modeling uncertainties on the nominally optimal excitation was also investigated. It is shown that using a theoretically optimal excitation, in practice, rarely generates the desired traveling wave due to modeling imperfections. This means that a stage of tuning the excitation to achieve a desired response is always necessary. A robust, open loop, travelling wave tuning method is proposed, but it is also shown that in some cases the forming of travelling waves is practically impossible due to specific dynamical behavior of the structure.

Another significant point, when dealing with traveling waves, is the identification of the existing wave pattern within a measured response of a structure. A wave is a spatio-temporal phenomenon, thus, both time and spatial measurements are required to assess the current wave pattern. Several methods were investigated for wave identification decomposition during the research. It was found that methods aimed at one-dimensional waves are not suitable for the identification of two-dimensional planar waves and different approaches should be used.

Finally, wave excitation methods were combined with wave identification methods in order to modify the structure’s response towards a desired traveling wave. The tuning is carried out using an optimum seeking approach, where a merit function represents how far the existing, measured response is from a pure traveling wave.

This work shows several numerical simulations and laboratory experiments of one and two dimensional structures to verify the developed theory and algorithms.