High‐order shape functions for interior acoustics

The acoustic behavior of structures has lately been in the focus of industrial applications, due to the fact that the acoustic emission of a product is one major parameter which significantly influences the customer perception with respect to comfort and functionality. In this context, the numerical simulation of vibroacoustic problems needs to provide reliable information in order to be able to evaluate the acoustic behavior of new products already in an early stage of the product development cycle. With the help of a suitable simulation model expensive experimental studies can be reduced and acoustically improved designs can be developed. However, there are already commercial software tools available which offer the opportunity to solve coupled vibroacoustic problems. These tools are typically based on conventional low‐order finite element methods ( h ‐FEM) for solving the governing partial differential equations (PDEs) of the problem. In this contribution, the advantages of high‐order finite element methods, such as a possibly exponential rates of convergence, will be exploited. Based on this approach a similar accuracy compared to classical h ‐FEM simulations using significantly less degrees of freedom (dof) can be achieved. Consequently, the computational time required for the analysis can be notably reduced for a given error threshold. Reducing the computational effort is of special importance when investigating complex structures of practical relevance. Even today, the overall efficiency of the simulation process is still an issue, despite the ever growing computational power. To exploit the described advantages, high‐order FEMs have to be extended to acoustical problems. In this contribution the developed high‐order simulation approach is discussed and the obtained results are compared to commercial finite element solutions focussing on the accuracy and the computational effort of the different approaches.