Characterizing Wave Behavior in a Beam Experiment by Using Complex Orthogonal Decomposition

Abstract

Complex orthogonal decomposition (COD) is applied to an experimental beam to extract the dispersive wave properties from response measurements. The beam is made of steel and is rectangular with a constant cross section. One end of the beam is free and is hung by a soft elastic cord. An impulse is applied to the freeend. The other end is buried in sand to absorb the wave as it travels from the impact site on the freeend; this effectively prevents reflections of the wave off the buried end and emulates a semiinfinite beam. The beam response is measured with an array of accelerometers, whose signals are integrated to obtain an ensemble of displacement signals. Acceleration responses are also compared in the frequency domain to predictions from the Euler–Bernoulli model. COD is applied to the displacement ensemble to obtain complex modal vectors and associated complex modal coordinates (COCs). The spatial whirl rates of nearly harmonic modal vectors are used to extract the modal wave numbers, and the temporal whirl rates of the modal coordinates are used to estimate the modal frequencies. The dispersion relationship between the frequencies and wave numbers compare favorably to those of the theoretical infinite Euler–Bernoulli beam.