Excitation and sensing of multiple vibrating traveling waves in one-dimensional structures

Lightly damped vibrating structures normally exhibit vibration patterns that are a combination of standing waves, i.e. mode shapes. Traveling waves, on the other hand, occur only under special circumstances. In this work, the theoretical conditions under which traveling waves prevail in finite structure are investigated. These conditions are highly sensitive to the geometrical and material parameters of the structure and in particular the vibration pattern is sensitive to the boundary conditions. There are several combinations under which traveling waves cannot be formed and these ill-posed cases are analyzed in some detail. To overcome the unavoidable uncertainties in a model, a tuning process based on identification and optimization of the excitation is suggested. The identification process uses a parametric algorithm to estimate the wavenumbers of the measured vibrations. Then, the waves are decomposed into traveling and standing parts and the external excitation is tuned until a pure traveling wave is formed.