A study on attenuation patterns of acoustic waves in waveguide structures with flexural boundaries

This research article investigates the attenuation patterns of acoustic waves within waveguide structures featuring flexural boundaries. By employing advanced methods in vibrations and controls, the study aims to enhance our understanding of waveguide behavior and offer valuable insights for optimizing acoustic wave propagation in diverse applications. The entire waveguide structure is tuned through cooperative interactions involving elastic plates, membranes, and rigid boundary surfaces. The lower boundary of the expansion chamber consists of a rigid plate, with elastic membranes covering the upper surfaces of the cavity. The problem is formulated in terms of transmission and reflection coefficients of the modes, enabling the solution of the scattering problem. Matching acoustic pressure and velocity at the waveguide junction yields the scattering coefficients. The results reveal that the scattering coefficients are intricately influenced by both the geometric characteristics of the waveguide and the frequency of the incident waves. Notably, the first higher-order mode of the cut-off frequency of the waveguide structure corresponds to the frequency at which the dissipation coefficient reaches its maximum value. This research provides valuable insights into the scattering behavior of acoustic waves in waveguide configurations, contributing to the design of acoustic devices and systems. Rigorous support and justification for all aspects of the mode-matching method, including pressure and velocity matching, eigen properties, physical edge conditions, convergence criteria, and energy conservation, are provided through thorough algebraic and numerical analyses, confirming the validity of the solution methodology.