DPSM Modeling for Studying Interaction Between Bounded Ultrasonic Beams and Corrugated Plates with Experimental Verification

Periodically corrugated structures play an important role in the field of vibration control and for designing structures with desired acoustic band gaps. Analytical solutions for corrugated plates are available for well-defined, smooth corrugations, such as sinusoidal corrugations that are not very common in the real world. Often corrugated plates are fabricated by cutting grooves at regular intervals in a flat plate. No analytical solution is available to predict the wave propagation behavior in such a periodically corrugated plate in which the equation of the plate surface changes periodically between a planar flat surface and a nonplanar parabolic groove. This problem is solved here for steady-state case by a newly developed semianalytical technique called distributed point source method (DPSM), and the theoretical predictions are compared with the experimental results generated by reflecting a bounded 2.25 MHz ultrasonic beam by a fabricated corrugated plate. The main difference that is observed in the reflected beam profile from a flat plate and a corrugated plate is that the back- scattering effect is much stronger for the corrugated plate, and the forward reflection is stronger for the flat plate. The energy distribution inside the corrugated plate also shows backward propagation of the ultrasonic energy.