An acoustic method for finding weak parts in wooden logs

摘要

This study presents a model of transverse vibrations in a log with a weak part. The aim is to use this model for the inverse application to find the weak part from measurements of transverse vibrations. More precisely, an optimization procedure based on the square of the difference, between measurements and simulations from the model is formulated. The error in the location of the weak part, caused by noise in measurements, can be reduced by including the spatial derivative of transverse vibrations in the optimization and by choosing an optimal frequency. It is shown that for a weak part with no spatial extension along the log, a weak layer, the optimal frequency is a resonance frequency. The a priori information that there is a weak part makes it possible to use wavelengths much longer than the size of the weak part.