Simultaneous measurement of thickness and bulk wave velocities of thin plates using laser-excited local ultrasonic resonances

Ultrasonic characterization techniques have been widely used for plates or plate-like structures in industrial applications and research development. Complex real situations pose challenges to the existing methods, such as in-situ measurement for fast and in-service evaluation, simultaneous determination of thickness and wave velocity when both variables are uncertain, multi-mode characterization for complete elastic properties, and local measurement for inhomogeneous variations. This study is based on non-contact laser ultrasound, utilizing the wideband characteristics to obtain the multi-mode local ultrasonic resonance spectrum of thin plates, including bulk wave-based thickness resonance modes and zero-group-velocity (ZGV) Lamb wave resonance modes. Firstly, theoretical solutions of local ultrasonic resonances are obtained in the dimensionless form with Poisson's ratio as the only variable. Secondly, a modified least-square minimization algorithm is used to search the theoretical solutions with multiple experimental resonant frequencies. Then, Poisson's ratio and relative wave velocities with respect to the thickness can be calculated. Finally, the spatial distribution of the first ZGV mode is measured by limited local scanning around the excitation spot. Through matching the theoretical wavefield pattern, the thickness is obtained and wave velocities are decoupled. This method can be applied to thin structures with only single-side access. The local scanning range required is no more than one wavelength of the first ZGV mode or twice the thickness for most usual materials, rendering local measurement for thin structures. The influence of the spot size of the excitation laser is discussed theoretically and experimentally. Such a method can be used to image the non-uniform thickness and elastic properties, such as localized plastic deformation.