Optimizing noise control in flexible shells with bridging membrane discs variations

This study explores the acoustic behavior of flexible cylindrical shells incorporating membrane discs at structural interfaces, focusing on their influence on wave propagation characteristics. The dynamics of the embedded membrane discs are modeled at the junctions between different shell segments, and the resulting boundary value problem is addressed using a combination of the Mode-Matching (MM) and Galerkin methods. The governing equations comprise the Helmholtz equation in the fluid domain and the Donnell-Mushtari shell equations in the elastic guiding regions. To ensure the accuracy and convergence of the semi-analytical solution, generalized orthogonality conditions are employed. A truncated modal expansion is used to reconstruct the matching conditions and enforce physical conservation laws at the interfaces. Numerical simulations are conducted to examine the effects of geometric parameters-such as the radii of adjacent shell segments, the size of the membrane discs, and the excitation frequency-providing valuable insights for the design and optimization of waveguide-based acoustic attenuation systems.