In this work, the vibrations of a structure excited by an impact source are modelled using the time domain nodal discontinuous Galerkin (DG) method, which solves linear elasticity equations. A scaled lightweight wooden floor (LWF) structure which consists of components that differ in their mechanical properties is taken as a case study. The Rankine-Hugoniot jump conditions for piece-wise constant material properties are used to obtain accurate numerical fluxes in the DG method, and their detailed derivation is the main contribution of this work. Free boundary conditions are applied on the surface of the structures, and constant viscous damping force is added to the model to have vibrational energy losses. To validate the numerical results, the mobility of the structure is calculated and compared with experimental data. The agreement is good regarding the natural frequencies, with a maximum absolute difference of less than 11 Hz in the frequency range below 200 Hz. The adopted damping approach is shown to be insufficient to represent a broad frequency range.@en

This study presents numerical solutions for two vibroacoustic problems using the time-domain nodal discontinuous Galerkin (DG) method. The first problem is the impact sound radiation from a rectangular slab into a cuboid room, and the second is the sound transmission between two cuboid rooms with direct and flanking contributions. The structures are modelled as a three-dimensional solid governed by the linear elasticity equations, and sound propagation in the rooms is governed by the linear acoustic equations. In the impact sound radiation case, the normalised sound pressure is evaluated and compared to the one obtained by the modal expansion method. In the sound transmission case, pressure transfer functions between different positions are calculated and compared to those obtained by the finite element method (FEM). The upwind numerical fluxes in DG for both governing equations, as well as the coupling conditions, are presented. There is excellent agreement between the solutions obtained by the nodal DG and those obtained by the modal expansion method/FEM. Although minor discrepancies exist in the resonance frequencies and magnitude, the overall trend shows good agreement.@en