Modeling and analysis of scattering in trifurcated guided waves with hard and flexible outer surfaces: A mathematical study

Abstract This article discusses the scattering in a trifurcated guided wave featuring the combination of hard and flexible exterior surfaces. Through the formulation of the relevant boundary value problem and modes matching of orthogonal and non‐orthogonal functions, a comprehensive solution is obtained through infinite linear algebraic equations. The structural complexity of these structures introduces challenges related to non‐linearities in dispersive relations, and uncommon orthogonal characteristics of eigenfunctions. Therefore, by reorganizing the differential system into an algebraic one, a solution is obtained by truncating the system numerically. Further, analytical and numerical tests validate the solution, including graphical representations of relative powers versus frequency. The results reveal that transmission dominates reflection for frequencies above 900Hz in the symmetrical setting, with nearly equal power propagating through regions 2, 3, and 4. In the non‐symmetrical setting, power primarily transmits through region 4 for frequencies above 600Hz whereas most of the power being reflected at cut‐on frequencies when region 3 as rigid‐soft instead of rigid‐rigid. The obtained solution also confirms the properties of eigenfunctions, and the power distribution among different regions validates the accuracy of the solution. This work holds significance as it provides a standard procedure for modeling and solving a broad range of multifurcated problems with multiple dynamic boundary properties. The findings aid the understanding and development of waveguide systems, offering vision to practical applications in various fields involving complex wave propagation.