Acoustic analysis and design of compliant cable-hose systems

Starting with basic equations of mass continuity and momentum balance, incorporating viscous damping, the finite radial impedances of the cable as well as the hose, and the convective effect of mean flow, coupled wave equations have been derived for waves inside the cable and also in the annulus of a cable-hose system. These have been solved together as an eigenvalue problem, and thence a 4 × 4 transfer matrix has been derived. Applying appropriate boundary conditions, the desired 2 × 2 transfer matrices have then been derived for the extended inlet and extended outlet type of elements. Then, axial transmission loss has been calculated for a typical cable-hose configuration and has been compared with that computed by the classical equivalent sound-speed model in vogue, which has been shown here (as well as earlier for hoses) to be a special case where the tube wall is assumed to be elastic but massless. Finally, the effect of breakout noise on the design of cable-hose systems is discussed.