Determination of the dispersion relation in cross-laminated timber plates: Benchmarking of time- and frequency-domain methods

The availability of a reliable estimate of the dispersion relation of plates is of great importance for acoustic modelling. Several experimental methods for the extraction of wavenumber and wave velocity information are discussed in the literature. They differ, among other factors, by the sensitivity to noise and multiple reflections, frequency range of application and implementation of the processing algorithm. While for homogeneous thick or thin plates well-established analytical solutions are available, non homogeneous materials would benefit from experimental characterisation. In this framework, our attention is focused on cross-laminated timber (CLT) elements, load-bearing orthotropic layered wood plates that revolutionised the sector of timber construction. The anisotropic and non homogeneous nature of wood suggested testing methods that, though converging for homogeneous materials, could bring different results in their application to CLT elements. The aim of this paper is therefore to benchmark methods for the extraction of wavenumber information on CLT plates, from which the effective elastic properties to model CLT structures as an equivalent homogeneous plate can be derived. This is achieved through a numerical and experimental benchmark of well-established methods for the evaluation of the real component of the propagating wavenumber in CLT elements. Five relevant methods were selected through a literature review, implemented and analyzed: three in the time domain, namely maximum peak, cross-correlation and kurtosis, and two in the frequency domain: phase difference and wave correlation. First, the five methods were benchmarked by numerical simulation on a homogeneous material. In this ideal case, results showed to be consistent for all methods. Then, wavenumber measurements were performed on a cross-laminated timber plate. The results show that the maximum peak, cross-correlation and the wave correlation method provide the lowest dispersion of the data. Considering the time required by the installation of the setup, the wave correlation method seems to be the best alternative among the proposed ones.