# Numerical Analysis of Vibroacoustic Response of Timber Floor Panels Damped with Porous Materials
## 1 Introduction  
A timber floor panel is a construction element that is typically made up of a layer of timber or wood-based material, which is often supported by a framework of wooden joists or beams. Timber floor panels are commonly used in residential and commercial buildings as a structural and finishing element for floors, and they may also serve as a base for other types of flooring materials, such as carpet, tile, or hardwood. Acoustic and vibration design of timber floor panels is an important consideration in building design, and can have significant impacts on the comfort, safety, and sustainability of a building over its lifespan [1]. A timber floor panel with poor vibroacoustic properties can lead to high levels of noise and vibration transmission between floors, which can be disruptive and lead to a lack of privacy and productivity. It can also affect the structural integrity and durability of the timber floor panel over time, causing fatigue and damage to the timber. The introduction of damping materials is an important technique for reducing vibration and improving sound insulation in timber floor panels. Vibration caused by impact or walking can create noise and discomfort for building occupants. Damping materials, such as viscoelastic layers or porous materials [2], can absorb sound and vibration energy, which helps to dampen the panel's natural frequencies and reduce its resonance. On the other hand, the connection between the timber floor panel and the supporting structure is another important factor in the vibroacoustic behavior of such a structure [3]. A rigid connection(boundary conditions) can help to distribute the load evenly across the panel and prevent it from vibrating excessively as it reduces the deflection of the panel [4; 5]. In contrast, a weak or flexible connection can allow the panel to move more freely, which can increase the amount of vibration and sound transmission. Eurocode 5 [6] specifies the serviceability limit states (SLS) for timber floors based on vibrational factors such as fundamental frequency, unit point load deflection, and unit impulse velocity response. Furthermore, the methods for calculating these characteristics are suggested in the National Annexes of the European nations, which vary greatly from one another due to differences in design approaches, manufacturing operations, and building techniques. The common suggestion is that the vibrational performance of the floor is controlled by assuring the fundamental natural frequency is greater than 8 Hz, and through limiting the deflection under the unit point load and the unit impulse velocity response. The vibration response of different types of floor systems (composite, concrete, steel with timber) was identified under the action of human activities [7; 8; 9; 10; 11]. Damping ratios were found to be in the range of 0.5% to 1.3% for any of the first five first-order principal modes. [PERSON] [12] investigated the effect of various structural modifications on the rigidity and dynamic response of timber flooring systems constructed with I-joists or laminated glued lumber (LGL) joists. Nowadays, a lot of researchers have started to investigate the vibroacoustic of timber floor panels. [PERSON] et al. [13] present an analysis of the vibroacoustic properties of cross-laminated timber (CLT) panels using wave and finite element (WFE) methods. The study compares two WFE modeling approaches to a commonly used orthotropic plate model. The research finds that the models are in good agreement at low frequencies but diverge at higher frequencies, where the vibroacoustic behavior of the panel becomes more complex. The paper concludes by comparing predicted results to experimental measurements and assessing the impact of uncertainty in different structural material properties on sound-transmission loss. [PERSON] et al.