Generalized analytical dispersion equations for guided Rayleigh-Lamb (RL) waves and shear horizontal (SH) waves in corrugated waveguides

Abstract

Corrugated waveguides are periodic structures that exhibit important acoustic features. Features like acoustic bandgaps exhibit the ability to filter acoustic and ultrasonic frequencies. By varying the mean thickness, corrugation height, and periodicity, one can tune the propagating wave modes in the guide and thus can modify the bandgaps. This study aims to obtain a generalized Rayleigh–Lamb equation for corrugated waveguides such that a single equation is sufficient for both flat waveguides such as plates as well as corrugated and tapered plates. Further, the objective was to understand the effects of the corrugation height, periodicity, and mean thickness such that a physics-based predictive design of wave filters can be achieved. Instead of applying the Bloch–Floquet theorem to the displacement function directly, which is conventional, the theorem is applied to the scalar and vector wave potentials obtained from Helmholtz decomposition. The governing equations from these relationships after applying boundary conditions were then solved using a logical root-finding algorithm. To verify the generalized expressions guided wave band structure for a plate was obtained using Rayleigh–Lamb equation and compared with the generalized form setting the corrugation height to zero. The analytical solutions are then validated through a comparison with the results obtained from a rigorous finite element simulation. Finally, the effects on the propagating and evanescent wave modes due to the corrugation height and periodicity are studied for future reference.