On the diffuseness of the vibrational field of a cross-laminated timber plate: Comparison between theoretical and experimental methods

The modelling of vibro-acoustic properties of plates usually requires the hypothesis of diffuse conditions of the vibrational field. For heavy-weight homogeneous isotropic plates, this condition is met starting from low frequencies. Nevertheless, the same hypotheses do not hold when applied to stiff, inhomogeneous and non-isotropic materials, like wood, thus its modal behavior needs to be addressed with more detail. The aim of the work is to benchmark theoretical methods and experimental measurements that allow to estimate when the transition from modal to diffuse field occurs in Cross Laminated Timber (CLT) elements. For this purpose, the diffuseness of the vibrational field has been investigated through the experimental evaluation of the mode count and the modal overlap factor on a pilot CLT panel. Measurements of the spatial distribution of modes, impulse responses, dispersion relations and driving point admittance were conducted in laboratory on an 8 m2 CLT plate. The analysis of the results allowed, on the one hand, to directly estimate the two parameters, and on the other, to provide input data necessary to evaluate and compare different theoretical models. Results of direct measurements, performed up to 550 Hz, show that the number of modes occurring in one-third octave bands exceeds the standard threshold of 5 only at 500 Hz, whereas the modal overlap factor is lower than the standard threshold of 1 for most of the modes. This indicates that the vibrational field is mainly non-diffuse in the mid-low frequency range, due to the small number of modes combined with a low damping of the CLT plate. Nonetheless, measurements of modal reverberation time and structural reverberation time in one-third octave band provided consistent results, implying that modal decays are the major contributors to the one-third octave band decay. Furthermore, comparisons with theoretical models show that the driving point admittance proved to be the best method of analysis, requiring simple measurement setup and signal processing, whereas the ISO 10848-4 is affected by the thin plate hypothesis and underestimates the mode count at mid-high frequencies.