Vector control method applied to a traveling wave in a finite beam.
Progressive flexural waves can be generated only in finite structures by fine tuning the excitation and the boundary conditions. The tuning process eliminates the reflected waves arising from discontinuities and edge effects. This work presents and expands two new methods for the identification and tuning of traveling waves. One is a parametric method based on fitting an ellipse to the complex spatial amplitude distribution. The other is a nonparametric method based on the Hilbert transform providing a space-localized estimate. With these methods, an optimization-based tuning of transverse flexural waves in a one-dimensional structure, a vibrating beam, is developed. Existing methods are designed for a single frequency and are based on either combining two vibration modes or mechanical impedance matching. Such methods are limited to a designated excitation frequency determined by a specific configuration of the system. With the proposed methods, structural progressive waves can be generated for a wide range of frequencies under the same given system configuration and can be tuned in real time to accommodate changes in boundary conditions. An analytical study on the nature of the optimal excitation conditions has been carried out, revealing singular configurations. The experimental verification of the sensing and tuning methods is demonstrated on a dedicated laboratory prototype. The proposed methods are not confined to mechanical waves and present a comprehensive approach applicable for other physical wave phenomena.