# Numerical Analysis of Vibroacoustic Response of Timber Floor Panels Damped with Porous Materials
## 2 General Structural Design
### Experimental and Numerical Determination of the Mechanical Properties of Glued Laminated Timber  
Glued laminated timber, commonly referred to as glulam, is a structural timber product made from glued smaller pieces of wood elements. Glued laminated timber can be produced in either a straight or curved form, with the grain of all laminations essentially parallel to the axis of the member. A supporting standard, Table 1 of BS EN 338:2009 [19], contains the material property values. Eurocode 5 [6] addresses the material properties and defines the strength and stiffness parameters, stress-strain relations, and provides values for modification factors for strength and deformation according to various service classes and/or load-duration classes, but it does not contain the material property values.  
Four-point bending tests have been conducted until the failure of the beams (glulam GL24h, which consists of 4 layers) at 2.30 m long and a cross-section of 90 \(\times\) 180 mm (Figure 2). Seven different sequences have been conducted and the envelope of the experimental curves is presented in Figure 3. During the experimental set up the deflection was measured using a linear variable differential transformer (LVDT), located on both two sides of the beam in the middle of the span (Figure 2). The total deflection was calculated as the mean value of both measurements, and the failure load was registered. These experimentally derived material properties were utilized in the subsequent numerical study.  
Numerical models, using the finite elements method (FEM), were developed and the FEM model geometry reproduced the actual geometry of the experiments. In addition, the simulation used the same boundary conditions and loading as in the experimental program. The physical and mechanical properties, obtained from the previous experimental tests, were used as input data in the FEM model. The modulus of elasticity perpendicular to the grain (\(E_{90}\)) was estimated according to Equation (1) [20].  
\[E_{90}=\frac{E_{0}}{30} \tag{1}\]  
where \(E_{0}\) is the modulus of elasticity parallel to the grain.  
Elastoplastic orthotropic material models were used with non-linear hardening associated with material densification. The orthotropic material parameters were optimized to match the experimental force-displacement curves, while the densities were determined by weighing the specimen and measuring their dimensions. Table 1 summarizes the details of the material properties. \(E_{1}\) is the [PERSON]'s modulus along axis 1 (axis 1 is the axis parallel to the wood grain), \(E_{2}\) is the [PERSON]'s modulus along axis 2, and \(E_{3}\) is the [PERSON]'s modulus along axis 3. The assumption that \(E_{2}=E_{3}\) has been made in this study (axes 2 and 3 are the axes perpendicular to the wood grain). \(f_{m,k}\) is the bending strength, \(v_{12},\ v_{13},\ v_{23}\) is the Poisson ratio in the planes 12, 13, and 23, respectively, while \(\rho\) is the characteristic density.  
The comparison of the experimental results with the numerical ones in terms of force-displacement curves are illustrated in Figure 3. The difference between the experimental and the numerical results for displacements after the maximum bending strength is related to the structural adhesives between the layers of glued laminated timber and its failure mode (detachment of layers), which were not modeled in the present study. This work is focused on small floor displacements, in the elastic domain, so the outcomes are not affected.  
In the numerical model, the damping value of wood, which has been proposed by the EN 1995-1-1, is used [6] (\(\zeta=1\%\)).