Numerical simulation of the vibro-acoustic behavior of multi-layered panels
Zusammenfassung der Projektergebnisse
The main purpose of this project was to improve the numerical simulation of the sound transmission through multi‐layered panels, which can be composed of different plates, e.g. of elastic, poroelastic, or fibrous material. Very often, also thin “air layers” occur in the overall panel setup. Before the start of the project, numerous models did existed which were able to predict well the behavior of elastic plates by both 3‐D and 2‐D formulations. Since a 2‐D model can be discretized in a rather easy way and often has less degrees of freedom, it became the preferred choice for real life applications. An efficient 2‐D formulation of poroelastic and fibrous plates, however, did not exist yet. Therefore, within the current project a new formulation of poroelastic plates has been developed (TU Graz). It eliminates the thickness of the plate under investigation by approximating its dynamic behavior with a polynomial series. The same methodology is further used to develop a so‐called air‐plate formulation, which solves the acoustical problem in a thin layer of fluid. It is noteworthy that the air‐plate model is not only valid for air gaps between multi‐layered panels, but also for some fibrous plates, since those fibrous materials can be regarded as a fluid with specific acoustical properties. With the help of the newly developed plate models, the sound transmission of multi‐layered panels can be completely simulated by plate elements. This means that no matter how many layers are included, each can be modeled with a single layer of 2‐D elements. In order to effectively solve the problem, an iterative coupling strategy and a multi‐frequency solution are proposed. These, however, are best suited for rather simple systems, and partially the methods are only applicable for acoustical problems. In view of this, a new solving strategy has been suggested in the current project, namely a multi‐frequency solver based on the Krylov subspace recycling solver. It is called Generalized Conjugate Residual with inner Orthogonalization and Deflated Restarting (GCRODR). Such a solver is designed to solve systems of equations where the coefficient matrices are similar, as in the case of those matrices arising for adjacent frequencies. By reusing the subspaces, the inter‐frequency solving is accelerated considerably. However, the systems of multi‐layered panels are often ill‐conditioned. This requires a proper preconditioner; otherwise the system can hardly be solved by Krylov subspace methods. Taking the advantage of the fact, that the multi‐layered panels are coupled in series, the complete system is decomposed by using the Schur complement method. Each subsystem presents a layer of the panel. Using the Algebraic Recursive Multilevel Solver (ARMS) as reference, the preconditioner is calculated by recursively decomposing the subsystems into their ILU/LU form. Furthermore, the new model is programmed in such a way that the panel can be composed of any number of layers with different materials. In order to demonstrate the accuracy and applicability of the new model, a panel with 5 layers including an air gap, elastic, poroelastic, and fibrous materials are simulated and validated by measurements. The current solving strategy is managed under a generalized framework. Technically, other subspace reusing solvers could be used instead. It would be of interest to see whether they could further improve the efficiency of the solving process. Another possible improvement for the solver is to develop a proper ILU‐type of decomposition for the poroelastic plate, where the complete LU is currently used. Finally, in the future, the plate models could be extended for thin structures with curvatures, such that more complicated models can be simulated as well.
Projektbezogene Publikationen (Auswahl)
- Higher order finite and infinite elements for the solution of Helmholtz problems. Computer Methods in Applied Mechanics and Engineering, 198: p. 1171‐1188, 2009
J. Biermann, O. von Estorff et al.
- An extendable poroelastic plate formulation in dynamics. Archive of Applied Mechanics, 80: p.1177‐1195, 2010
L. Nagler, M. Schanz
- Beschleunigung von MultifrequenzFEAnalysen durch dir Verwendung von Gleichungslösern mit „Subspace Recycling“. The 37th German annual conference on acoustics (DAGA), Düsseldorf, 2011
J. Biermann, O. von Estorff
- Simulation of Sound Transmission through Poroelastic Platelike Structures. Dissertation, TU Graz (2011)
L. Nagler
- Simulation of the acoustical behavior of reverberant room by means of the fast multipole BEM. The 37th German annual conference on acoustics (DAGA), Düsseldorf, 2011
P. Rong, O. von Estorff
- A new preconditioner for the iterative solution of the systems describing the vibroacoustics of multilayered panels. The 38th German annual conference on acoustics (DAGA), Darmstadt, 2012
P. Rong, O. von Estorff
