Fluid-structure coupled wave scattering in a flexible duct at the junction of planar discontinuities

Rab Nawaz,Muhammad Afzal,Aasim Ullah Jan

doi:10.1177/1687814017713187

Abstract

This article applies the mode-matching technique to discuss acoustic scattering of waves in flexible duct/channel at the junction of planar discontinuities. Fields across the junction are expanded in normal modes that involve discontinuities in velocities at the flanged junction. The reflected and transmitted fields are matched at interface wherein the use of generalized orthogonal properties (in case of flexible bounded ducts) enables the mode coefficients in terms of system of infinite linear algebraic equations. This system is truncated and solved numerically. The numerical experiments show that the variation of structural discontinuities along with different bounding surfaces significantly alters the reflected and transmitted powers.

Highlights

There are numerous problems in the field of structural acoustics, elasticity, electromagnetic wave theory, water wave, and so on, where we deal with the propagation of waves in duct or channel.[1,2,3,4,5,6,7,8,9] In many problems, such ducts or channels contain structural discontinuities and different bounding material properties, for instance, a silencer design, where there is a coating and the abrupt geometric changes in bounding surfaces to minimize the noise transmission
The boundary value problems of the type governed by Helmholtz’s or Laplace equation immersed with boundary conditions of Dirichlet, Neumann, or Robin type are tractable using the mode-matching (MM) technique
The separation of variables method allows the superposition of evanescent normal modes with unknown mode coefficients in each region of duct/channel containing constant material properties

Summary

Introduction

There are numerous problems in the field of structural acoustics, elasticity, electromagnetic wave theory, water wave, and so on, where we deal with the propagation of waves in duct or channel.[1,2,3,4,5,6,7,8,9] In many problems, such ducts or channels contain structural discontinuities and different bounding material properties, for instance, a silencer design, where there is a coating and the abrupt geometric changes in bounding surfaces to minimize the noise transmission. The aforementioned systems are solved numerically after their truncation at N terms Such systems are non-SL in nature and converge suitably for the membrane and elastic plate–bounded ducts.[10,18] the truncated solution may be used to check the accuracy of presented algebra and distribution of energy flux. For structure borne-mode incident, almost all the incident power goes on reflection while excluding flange discontinuity with rigid, soft, or membrane surface at y = b, x 2 (0, ‘) (see Figure 6). This case is quite similar to the previously taken case discussed in the presence of flanged. Note that c1(0, y) and c2(0, y) coincide as h1\y\h2, while

Concluding remarks

Declaration of conflicting interests