Smooth complex orthogonal decomposition applied to traveling waves in elastic media

Abstract

A novel method called smooth complex orthogonal decomposition (SCOD) was applied to a simulated infinite beam and an experimental beam that emulated a semi-infinite beam. The beam was instrumented with accelerometers, and the accelerations were numerically integrated to compute displacements and velocities. These measurements were converted into complex analytic displacements and velocities ensembles, which were used to compute two correlation matrices. These correlation matrices formed a complex generalized eigenvalue problem whose eigenvalues and eigenvectors led to the extractions of the frequencies and wavenumbers of the constituent waves of the traveling pulse. SCOD directly extracts the frequencies of the traveling waves from the eigenvalues. SCOD was able to extract the geometric relationship, phase velocity, and group velocity, and agrees with analytical predictions.