Time-domain structural vibration simulations by solving the linear elasticity equations with the discontinuous Galerkin method

In the field of building acoustics, an efficient solution of the linear elasticity equations for vibro-acoustic problems is of interest. The focus of this work is on the structural part, with plate vibra-tion problems in particular. The linear elasticity equations in the stress-velocity formulation are solved in the time-domain for the three-dimensional plate problem. The numerical solution is obtained through the Runge-Kutta discontinuous Galerkin method, which has the potential to be highly parallelizable and thereby computationally very efficient. Numerical aspects of applying the discontinuous Galerkin method to this problem are discussed, especially on the force excita-tion and the boundary conditions of the plate problem. The accuracy of applying the discontinu-ous Galerkin solution is presented by comparing its results to results from analytical solutions. Several scenarios of plate variations with different boundary conditions are simulated to demon-strate the capabilities of the method.