Modeling of orthotropic plates out of cross laminated timber in the mid and high frequency range

Abstract Within the context of efficient and sustainable design of buildings a trend towards lightweight structures, e.g. timber structures, is recognizable. This trend implies the necessity of being able to predict serviceability and comfort as well as sound transmission in order to fulfill vibroacoustic requirements. To generate reliable prediction methods, the transfer of energy between building components has to be investigated. Therefore, a detailed understanding of the modeling of the building components, e.g. walls or ceilings, is compulsory. In the low frequency range the Finite Element Method (FEM) is a convenient tool to predict the vibroacoustic behavior. However, without appropriate post-processing it is limited due to the sensitivity of the results at higher frequencies. In the mid-frequency range a sufficient number of modes per band enables the use of statistical methods like the Statistical Energy Analysis (SEA). It delivers averaged results and thus copes with the sensitivity. As both techniques have a restricted validity regarding the frequency range, averaging techniques of the SEA are applied in the post-processing of the FEM to obtain an adapted hybrid approach, the Energy Flow Analysis. This contribution will focus on the Finite Element Model of the building components out of cross laminated timber modeled as orthotropic plates. The Young’s modulus of wood is perpendicular to the fiber comparatively low, which leads to low velocities of longitudinal and shear waves. Hence, at high frequencies thickness-stretch and thickness-shear modes play an important role. These can be activated already at low frequencies within the stiffness controlled region of their amplification function. Hence, their non-resonant contribution can be identified evaluating the potential energy compared to the kinetic one. This phenomenon is verified with the help of solid elements - in comparison with shell elements - by varying the points of excitation across the thickness. Moreover, the dimensions will be modified as well as the junction by inserting an elastic layer. Whereas the SEA is typically not able to represent through-thickness effects of plate-like structures, the energy flow between a wall and a ceiling will be investigated using the hybrid approach.