Elastic characterization of wood by Resonant Ultrasound Spectroscopy (RUS): a comprehensive study

The main principle of Resonant Ultrasound Spectroscopy (RUS) measurement method is to excite a sample and to deduce its elastic constants from its free mechanical resonant frequencies. The goal of this paper is to propose an application of RUS in the case of wood cubic samples by: (1) using frequencies and mode shapes (or vibration patterns) of the free resonant modes in an iterative numerical procedure to solve the inverse problem for identifying components of the stiffness tensor of the sample's material, (2) finding the limits and optimizing the robustness of the identification procedure in the case of wood and (3) applying it to a large density range of wood samples. Specific continuous waves have been used as excitation signal in order to experimentally determine the free resonant frequencies and mode shapes of the sample in a faster way by means of Scanning Doppler Vibrometer measurements. Afterward, the stiffness tensor was derived by solving iteratively an inverse problem. The gain of using the mode shapes in the inverse identification procedure is demonstrated to be particularly necessary for wood, especially for pairing each measured frequency with its corresponding theoretically predicted one, as viscoelastic damping causes the resonant peaks to overlap and/or disappear. A sensitivity analysis of each elastic constant on the measured resonant frequencies has thus been performed. It shows that, in its current state of development, not all of the elastic constants can be identified robustly and a modified identification procedure is thus proposed. This modified procedure has been applied successfully to wood samples with a large density range, including softwood and hardwood, and particularly non-homogeneous wood species or with specific anatomical features.