# FEM based prediction model for the impact sound level of floors

Phd students: |
Dipl.-Ing. Andreas Rabold |

Principal investigators: |
Prof. Dr.- Ing. Alexander Düster |

Prof. Dr. rer.nat. Ernst Rank | |

Poject partners: |
ift Rosenheim |

Fraunhofer Institut für Bauphysik | |

Sponsorship: |
AiF coordinated by the |

Deutsche Gesellschaft für Holzforschung |

**Project description:**

Up to now the research and development in the field of building acoustics is based mainly on measurements. The consequence is that the development and optimization of a new building component is a very tedious and expensive task. A considerably reduction of these costs could be achieved, if the optimization relying on measurements would be replaced – at least to some extent – by a computational prediction model. Motivated by these aspects a method is developed for using finite element techniques to estimate the impact sound level from lightweight floors. The overall approach consists of the three-dimensional modeling of the structure and the excitation source (tapping machine), the subsequent modal- and spectral analyses and the computation of the radiated sound from the ceiling.

Excitation of the impact-sound:

In the experimental rating of the impact sound level of a floor the tapping machine is most commonly used as the excitation source. For the computation model the excitation force has to be expressed with respect to the interaction between the hammer of the tapping machine and the floor surface at the driving point.

Modeling of the structure:

The thin-walled lightweight floor, consisting of plates and beams is discretized with a fully three-dimensional approach, where anisotropic high-order solid finite elements are applied allowing different polynomial degrees for each direction of the element.

Modal analysis:

In the modal analysis the eigenvectors of the problem are computed and used to decouple the system of differential equations. In the second step the differential equations are Fourier-transformed and solved in the frequency domain. Due to the fact that the impact sound level of lightweight floors is dominated by transmissions at very low frequencies, the computation can be restricted to a small number of eigenvalues.

Impact sound spectrum:

The response of the structure to the excitation force spectrum with respect to the modal damping of the structure is computed in the frequency domain by summing up the result of each transformed differential equation. This computation is done for each excitation-position of the tapping machine and each considered radiation-point of the structure.

Radiation of the impact sound:

For the assessment of the impact sound insulation of floors the normalized impact sound pressure level Ln is calculated from the sound pressure level in the receiving room. In the prediction model, this quantity is computed from the radiated impact sound spectrum in different ways.

Fig.1: survey of computation | Fig.2: Comparison measurement – computation. a) computation using a modal method for the radiation b) computation using an integral method for the radiation c) measured data of similar floors in different test facilities d) mean value of measured data ± 2s |

**Publications:**

Rabold, A., Scholz, D., Rank, E., Berechnung der Trittschalldämmung von Holzbalkendecken mit der Finiten Elemente Methode,

Tagungsband Forum Bauinformatik 2004, Braunschweig

Rabold, A., Scholz, D., Rank, E., Berechnung der Trittschalldämmung von Holzbalkendecken mit Finite Elemente Methoden,

Tagungsband DAGA 2005, 487-488

Rabold, A., Düster, A., Rank, E., Anwendung der Finiten Elemente Methode auf die Trittschallberechnung von Holzdecken,

Tagungsband DAGA 2007

Rabold, A., Düster, A., Berücksichtigung der Dämpfung bei der Trittschallberechnung auf Basis der Finite Elemente Methode,

Tagungsband DAGA 2008, 411-412

Rabold, A., Düster, A., FEM based prediction model for the impact sound level of floors,

Conference proceedings EURONOISE 2008

Contact: Dipl.-Ing. Andreas Rabold