On Vibrating Traveling Waves Actuation, Sensing, and Tuning in Finite Structures

This work is concerned with a method to generate pure traveling vibration waves in finite structures. Using progressing deformations, i.e. waves, is not common when dealing with forced vibration since structures are naturally vibrating in their, naturally occurring, normal modes. Indeed, natural vibration modes can be referred to standing waves. Since a structure does not lend itself to a traveling wave vibration, the generation of traveling waves in a structure becomes a challenging task. The boundary conditions or external forces must be carefully tuned in an iterative process that necessitates measurement and identification of the traveling and standing wave components. In this work, a method to generate and measure traveling waves is presented for one and two-dimensional structures. Both analytical and experimental results are provided here. A traveling wave is a disturbance that propagates away from its source carrying energy along its path. In finite structures, a wave hitting a boundary experiences an impedance change that gives rise to a partial reflection, thus distorting its original form. For a pure traveling wave to occur, the boundary of the structure must be set to match the impedance of the structure, and thus to absorb the disturbance while preventing any reflected wave from the boundaries. Impedance matching can be accomplished by passive or active means. Active impedance matching is obtained by generating a vibrating wave at one end (a source) and 'pumps' it on the other, active absorbing end, often addressed as a sink. Indeed, active impedance matching sometimes referred as the "active sink" method. Special methods must be used to extract the description of the vibrating wave characteristics from the measured vibration efficiently, and possibly in real-time (for control purposes). A parametric method is employed in this work to describe and analyze the wave vibration from measurements. In reality, the theoretical knowledge of how to excite a vibrating traveling wave is not sufficiently accurate to produce traveling waves. Minute manufacturing imperfections, small structural and actuator asymmetry may cause large deviations from pure traveling waves state. It is shown that a tuning process that relies on the measurements but combined with a physical model, should serve as the basis of the practical implementation. Several experiments on a string-like structure are described stressing the physical implications as well as the refined experimental procedure. The actuation techniques, wave identification methods and the tuning procedure of a vibrating traveling wave are described in some detail for the experimental work.