Acoustic-Structure Simulation of Exhaust Systems by Coupled FEM and Fast BEM

The sound properties of modern cars play an increasingly important role on the overall impression of a vehicle. One of the major sound sources is hereby the exhaust system, which is exposed to large pressure pulsations resulting from the periodically blown out exhaust gas of the car engine. These large pressure pulsations lead to vibrations of the thin walls of the exhaust system and thus create another sound source which is additionally contributing to the sound radiation of the exhaust system besides the sound at the orifice. In this work, the sound radiation of an associated simplified exhaust system is analyzed. The sound transmission of the interior exhaust system is simulated by using conforming coupling of FE-FE-models. For the subsequent solution of the infinite exterior, problem the Fast-Multipole BEM is employed enabling a very fast and efficient computation. This work focuses on the contribution of the vibrating structure to the overall sound radiation. It is found that close to some resonance frequencies of the in-vacuo structure there is a significant contribution of the vibrating structure to the overall radiated sound power. Nomenclature F , F f load vectors u displacement degree of freedom Ia acoustic intensity vector W radiated soundpower I unity matrix vn normal velocity M s, Ks mass and stiffness matrix of the structure Z specific acoustic impedance M f, K f mass and stiffness matrix of the fluid Γ closed surface of radiating object M fs, K fs coupling matrices κ0 wave number n unit normal vector on boundary surface ρ, c density and wave speed of fluid P ∗ fundamental solution (V q)(x) single layer potential p pressure degree of freedom (Kp)(x) double layer potential q acoustic flux (K q)(x) adjoint double layer potential R complex reflection coefficient (Dp)(x) hyper-singular operator