Determination of the in-plane components of motion in a Lamb wave from single-axis laser vibrometry

A method is proposed for determining in-plane components of motion in a Lamb wave from laser vibrometer measurements of surface motion out of plane. The approach relies on a frequency domain transformation that assumes knowledge only of the plate thickness and the bulk wave speeds. An outline of the relevant theory is followed by several validation case studies that generally affirm a useful level of accuracy and robust performance across a relatively wide frequency-thickness product range. In a comparison to the two-angle vibrometry approach, the proposed method is shown to be simpler to implement and to yield estimates with a consistently higher signal to noise ratio. The approach is then used to furnish estimates of the in-plane strains in Lamb waves propagating in an aluminum plate at frequencies below the first cut-off. These estimates are compared to strain measurements obtained from an adhesively bonded fiber Bragg grating. The agreement is shown to be excellent overall with an average discrepancy of less than 6%; however, systematic errors of twice that amount were recorded in the low-frequency-thickness product regime. These low-frequency discrepancies are not consistent with known sources of experimental error and cannot be explained by shear-lag theory.