Measurement of phase accumulation in the transfer functions of beams and plates

Previous research into the phase of transfer functions from beam and plate-type structures has shown that the accumulated phase has different characteristics depending on whether the vibrational field is direct, diffuse, or between these two extremes. In this paper, these accumulated phase characteristics are numerically and experimentally investigated. Existing phase accumulation theories for direct and reverberant vibrational fields are presented. Predictions of the accumulated phase are then compared to measurements of the accumulated phase from the transfer mobilities of a number of beam and plate structures. It is shown that selection of the correct FFT frequency resolution in the experiment is vital in obtaining an accurate measurement of the phase of the transfer function. A criterion based upon the half-power bandwidth of the analysis frequency band is proposed as a basis to select the correct FFT frequency resolution. It is also shown that the location of the excitation may affect the measured value of the accumulated phase. Experimental results also show that the accumulated phase in a vibrational wave field between that of a direct field and a diffuse field is related to the source-receiver separation distance and to the damping in the structure. It is shown that the resulting accumulated phase curve lies between the direct field phase limit and the reverberant field phase limit.