Modal analysis of living spruce using a combined Prony and DFT multichannel method for detection of internal decay

Abstract:
Modal analysis is a widely accepted tool for non-destructive evaluation of mechanical properties of materials and structures. In this paper, a partial modal analysis is used to examine whether internal decay in living trees can be detected by studying the resonance frequencies of the trees. We examine the resonance frequencies of living spruce of species Picea abies (Norway spruce) by means of the pulse response due to the impact of a hammer onto the surface of the trunk. The response is measured by 12 accelerometers positioned around a cross-section of the tree, and modelled by sums of damped sinusoids. The temporal parameters are determined using Prony's method, and the spatial parameters associated to the circumferential mode shapes are determined using the discrete Fourier transform on the set of weights yielded by Prony's method. A total of 94 living trees have been examined. It is found that the mode shapes are almost clean sinusoids, and that reproducible results are obtained although the impact excitations are applied by hand force. The results show that a certain mode shape is found in recordings from all trees but one, and that it possesses the lowest temporal frequency in each tree. Furthermore, it is found that the temporal frequency of this mode shape often is lower for decayed trees than for sound trees, and that the difference in frequency seems to be related to the extent of decay. There is, however, a large scatter of the sound trees, which leads to a partial overlap of the two groups of sound and decayed trees. It is concluded that more parameters are required to further separate the groups from each other.