Spatial aliasing and false detection of standing waves in experimental determination of dispersion relationship by correlation method

Abstract

The experimental determination of a dispersion relation by measurements of wave properties in different points in space meets various challenges due to the spatial aliasing, which is a consequence of description of a continuous wave by a discrete set of measurement points. The paper presents an analysis of the phenomenon of false detection of standing waves during experimental determination of dispersion relationship of flexural waves in beams by correlation method. The false detection of standing waves, manifested as zero group velocity of the waves that does not correspond to a real resonance, is a consequence of equidistant spacing of measurement points in experimental setup, and may be avoided by different positioning of measurement points in space. The results of the analysis are verified by comparison between the results of experimental setups with equidistant measurement points and measurement points with distances to excitation point proportional to prime numbers.