Alahmadi Hani, Afzal Muhammad, Alkuhayli Naif
Department of Mathematics, College of Science, Jouf University, Sakaka, Saudi Arabia.
Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan.
PLoS One. 2025 Sep 5;20(9):e0328301. doi: 10.1371/journal.pone.0328301. eCollection 2025.
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.
本研究探讨了在结构界面处结合膜盘的柔性圆柱壳的声学行为，重点关注其对波传播特性的影响。在不同壳段之间的连接处对嵌入式膜盘的动力学进行建模，并使用模式匹配（MM）和伽辽金方法相结合的方式来解决由此产生的边值问题。控制方程包括流体域中的亥姆霍兹方程和弹性引导区域中的Donnell-Mushtari壳方程。为确保半解析解的准确性和收敛性，采用了广义正交条件。截断模态展开用于重构匹配条件并在界面处强制执行物理守恒定律。进行了数值模拟，以研究几何参数（如相邻壳段的半径、膜盘的尺寸和激励频率）的影响，为基于波导的声学衰减系统的设计和优化提供了有价值的见解。
