Discontinuous Galerkin method for vibration of structures with piecewise constant material properties

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.