A multiple-scale perturbation approach to mode coupling in periodic plates

In this paper, guided ultrasonic wave propagation is analyzed in an elastic plate with sinusoidal surface corrugations. The corrugated area acts as a finite-length grating which corresponds to a 1-D phononic crystal (PC). The multiple-scale perturbation technique is used to derive coupled-mode equations describing the amplitudes of interacting modes. These equations are solved exactly for the two-point boundary-value problem of the PC. The study involves the coupling of the incident symmetric Lamb wave S₀ to the reflected antisymmetric Lamb wave A₀. The influences of the depth of corrugation and length of the PC are studied. Theoretical results are compared with experimental measurements.