Shear Waves in an Initially Stressed Elastic Plate with Periodic Corrugations

The influence of the combined effect of initial stress and periodic surface corrugation on ultrasonic SH wave propagation in an elastic plate is investigated. Considering weak surface corrugations, a small parameter is defined using the ratio between the corrugation amplitude and the average thickness of the plate and the perturbation method of strained parameters is used up to the second order. An equation for evaluating the wave phase velocity in the periodically corrugated plate is realized. Numerical examples are provided to graphically illustrate the variations of the phase velocity in periodic plates, with various corrugation amplitudes and wavelengths, under compressive and tensile initial stresses over a frequency spectrum. The study reveals the dispersive nature of SH waves in corrugated plates. It is found that the wave phase velocities are slightly higher (lower) in plates under initial tension (compression) than initially stress-free plates. The influence of initial stresses on SH phase speed decreases as the frequency increases. It is shown that periodic surface roughness has a stronger effect on reducing wave phase speeds than a shallow surface waviness.