Spatial Laplace transform for complex wavenumber recovery and its application to the analysis of attenuation in acoustic systems

We present a method for the recovery of complex wavenumber information via spatial Laplace transforms of spatiotemporal wave propagation measurements. The method aids in the analysis of acoustic attenuation phenomena and is applied in three different scenarios: (i) Lamb-like modes in air-saturated porous materials in the low kHz regime, where the method enables the recovery of viscoelastic parameters; (ii) Lamb modes in a Duralumin plate in the MHz regime, where the method demonstrates the effect of leakage on the splitting of the forward S1 and backward S2 modes around the Zero-Group Velocity point; and (iii) surface acoustic waves in a two-dimensional microscale granular crystal adhered to a substrate near 100 MHz, where the method reveals the complex wavenumbers for an out-of-plane translational and two in-plane translational-rotational resonances. This method provides physical insight into each system and serves as a unique tool for analyzing spatiotemporal measurements of propagating waves.