Multimodal method for the scattering by an array of plates connected to an elastic half-space

Area of Science:

• Solid Mechanics
• Acoustics
• Materials Science

Background:

• Understanding wave propagation and reflection is crucial in materials science and engineering.
• Periodic structures significantly influence wave behavior, presenting complex analytical challenges.

Purpose of the Study:

• To develop an accurate and computationally efficient method for calculating in-plane wave reflection.
• To analyze wave interactions with elastic substrates supporting periodic arrays of plates.

Main Methods:

• Expansion of elastic fields using pseudo-periodic modes in the substrate and Lamb modes in the plates.
• Determination of unknown amplitudes via matrix inversion applying boundary conditions.
• Quantitative inspection of method convergence, considering stress singularities.

Main Results:

• Accurate calculation of wave reflection at the free surface of a substrate with periodic plates.
• Identification and analysis of two plate resonances: flexural and edge mode quasi-resonance.
• Demonstrated good convergence of the scattering coefficients (1/N_s^3/2) despite stress singularities.

Conclusions:

• The presented method offers an accurate and numerically inexpensive approach for wave reflection analysis.
• The method effectively captures complex phenomena like plate resonances and stress singularities.
• This work provides a valuable tool for designing and analyzing structures with periodic elastic elements.