Reciprocity-based closed-form solutions to guided waves in multilayered structures subjected to time-harmonic excitations

Ultrasonic guided waves provide an efficient tool for nondestructive evaluation and characterization of multilayered structures, e.g., of adhesively bonded joint in aerospace industry. In this article we investigate the propagation of guided waves in fully bonded multilayered plates excited by time-harmonic sources. By using the transfer matrix method, we propose explicit expressions of the free guided waves that depend on only one unknown constant representing amplitude. From these expressions, theoretical predictions of guided wave fields arising from a time-harmonic source are derived by using the reciprocity relations in elastodynamics. These very first closed-form solutions offer several distinct advantages, including efficient solution of inverse problems for materials characterization, direct calculation of guided waves at every point with a low computational cost and a benchmark to verify and improve numerical analysis of guided waves in multilayered structures. The obtained results are illustrated by computing guided wave motions in the bond region of an adhesively bonded lap joint, commonly used in automotive and aeronautical industries. The dispersion curves produced here are significant improvement upon those available in literature, as they are superimposed with the amplitude spectra values, enabling optimal selection of modes and frequencies for ultrasonic inspection. The analytical predictions of guided wave amplitudes in a three-layer adhesive joint model are numerically verified through finite element simulations, showing excellent agreement with the lowest guided wave modes.