A novel three-dimensional model for the prediction of ultrasonic velocity in wood considering its orthotropy

This paper deals with a three-dimensional model capable of determining the propagation velocities of ultrasound waves in wood. Considering simultaneously the three planes of orthotropy and using a spherical coordinate system, the mathematical expression of this model is proposed. The model is based on the two-dimensional Hankinson models commonly used for the characterization of velocities in each orthotropic plane. The model is composed of six (6) parameters. Three velocities in the main directions ( V L , V R and V T ) and three calibration coefficients ( l , m and n ) correspond to the three orthotropy planes. The experimental validation is based on ultrasonic measurements taken on a Douglas fir cube. A finite element support is used to recalculate the propagation velocities whatever the orientation of the propagation line by considering a cylindrical orthotropy induced by the construction of growth rings. The process of determining the model parameters ( V L , V R , V T , l , m and n ) by an inverse analysis algorithm is presented. The results show that the model improves the fit to the observed angular dependencies of the wave propagation velocities. The model predicts well the velocities outside the principal planes.