Re-expansion method for circular waveguide discontinuities: Application to concentric expansion chambers

Abstract

The paper applies the re-expansion method for analyzing planar discontinuities at the junction of two axi-symmetrical circular waveguides. The normal modes in the two waveguides are expanded at the junction plane into a system of functions accounting for velocity singularities at the corner points. As the new expansion has a high convergence order, only a few terms have to be considered for obtaining the solution of most practical problems. This paper gives the equivalent impedance accounting for nonplanar waves into a plane-wave analysis and also the scattering matrix describing the coupling of arbitrary modes at each side of the discontinuity valid in the case of many propagating modes in both sides of the duct. The last section applies the re-expansion technique to some concentric expansion chambers providing an explicit formula for the transmission loss coefficient.

Fluid–structure coupled response of dynamical surfaces tailored in a flexible shell

“…Note that in eigenfunction expansions given by equations ( 12), (13), and ( 23)-( 25), the amplitudes {B n , D n , E n }, n = 0, 1, 2, . .…”

“…By substituting equations ( 12), (13), and ( 23) into equation (30), after simplification through equation ( 27), it is found that:…”

“…On using equations ( 12), (13), and (23) into equations ( 36) and (37) and then simplifying with the help of orthogonality relations ( 16) and ( 17), we get:…”

“…For single and double ring constraints, the exact solutions of boundary value problems were achieved by converting the differential system to linear algebraic system. The wave scattering from discontinuities in a cylindrical duct was analyzed by Homentcovschi and Miles [13]. To formulate solution, the velocity field was expanded using the special functions that are useful to account the singular behavior at the edges.…”

Analyzing the impact of flexible shells and sound absorbent lining on acoustic wave behavior in ducts

“…This method entails matching the solutions of the wave equation at the interfaces between different regions of the waveguide, utilizing continuity conditions for both pressure and velocity. The mode-matching technique has gained wide acceptance in waveguide structure analysis due to its accuracy and efficiency, especially in cases involving nonuniform cross-sections and boundary conditions [16][17][18][19][20]. The primary objective of this study is to establish a theoretical framework for analyzing and optimizing the acoustic performance of the waveguide by employing the mode-matching method.…”