Tree vibrations: Determining oscillatory properties by using infra-red marker-tracking system

Abstract

A state-of-the-art infrared marker-tracking system that consists of eight cameras outfitted with infra-red optical filters and an array of infra-red light-emitting diodes as well as a set of reflective markers, is used to record the motion of a set of markers arranged along a trunk-dominated potted tree, which was pulled and released to perform free vibrations. The time-history diagrams of these markers are numerically fitted to the corresponding analytical mathematical model for each marker, in which the markers are treated as particles performing in-plane oscillations. This combination of experimental, analytical and numerical results yields the main vibration properties of the markers, i.e. the points on the tree: natural frequencies, damping ratios and the position of principal axes in two cases: for the in-leaf and out-of-leaf tree under consideration. The shape of the time history diagrams for the motion along one direction indicates the initial increase of the amplitude, and this property is found to be associated with two closed-valued natural frequencies. These two natural frequencies decreased after the removal of leaves, but stayed closed-valued. Two natural frequencies correspond to two principal axes, whose change along the height of the tree is also determined in both cases. The change of the damping ratios associated with two principal axes is also obtained: only one of them changed after the removal of leaves. Besides providing a proof of concept for the use of the high-tech marker-tracking system for obtaining certain oscillatory characteristics, this study also points out the possibilities for future work in which this system can be beneficial for investigating tree vibrations and deflections under different loads.