Characterisation of tree vibrations based on the model of orthogonal oscillations

The Kelvin-Voigt visco-elastic model involving a fractional-order time derivative for modelling torsional oscillations of a complex discrete biodynamical system

Under external loads trees exhibit complex oscillatory behaviour: their canopies twist and band. The great complexity of this oscillatory behaviour consists to an important degree of torsional oscillations. Using a system of ordinary differential fractional-order equations, free and forced main eigen-modes of fractional-type torsional oscillations of a hybrid discrete biodynamical system of complex structures were done. The biodynamical system considered here corresponds to a tree trunk with branches and is in the form of a visco-elastic cantilever of complex structure. Visco-elasticity corresponds to different ages of a tree. We set up a new model of torsional oscillations of a complex discrete, biodynamical system, using the Kelvin-Voigt visco-elastic model involving a fractional-order time derivative. The analytical expressions describing the characteristic properties of its fractional-type oscillations are determined. Based on mathematical and qualitative analogies, this concept represents a new model of torsional oscillations of a light cantilever that takes into account visco-elastic, dissipative properties of the material. Rigid discs are attached to the cantilever. Expressions for kinetic energy, deformation work and a generalized function of the fractional-type energy dissipation of this biodynamical system are defined. Independent main eigen-modes of the fractional type for free and forced torsional oscillations were determined for a special class of such systems, using formulas for the transformation of independent generalized angle coordinates to the principal main eigen-coordinates of the system. The forms of their approximate analytical solutions are shown. In the general case for inhomogeneous biodynamical systems of fractional type, there are no independent main fractional-type eigen-modes of torsional oscillations. The system behaves as a nonlinear system. A new constitutive relation between coupling of torsion loading to a visco-elastic fractional-type cantilever with fractional-type dissipation of cantilever mechanical energy and angle of torsion deformation is determined using a fractional-order derivative. The main advantages of the proposed model are the possibility to analyse torsional oscillations of more complex structures and the possibility to analyse complex cantilevers with different cross-sectional diameters.

Understanding the dynamic properties of trees using the motions constructed from multi-beam flash light detection and ranging measurements

Measuring the three-dimensional motion of trees at every position remains challenging as it requires dynamic measurement technology with sufficient spatial and temporal resolution. Consequently, this study explores the use of a novel multi-beam flash light detection and ranging (LiDAR) sensor to tackle such a sensing barrier. A framework is proposed to record tree vibrations, to construct the motions of tree skeletons from the point-cloud frames recorded by the LiDAR sensor and to derive the dynamic properties of trees. The feasibility of the framework is justified through measurement on a Ficus microcarpa under pull-and-release tests. The relative differences for the first two modal frequencies between the LiDAR and linear variable differential transformer measurements in the displacement Fourier spectra are 0.1% and 2.5%, respectively. The framework is further adopted to study the dynamic response of different trees subjected to typhoons, including a Liquidambar formosana, three Araucaria heterophylla trees, a Sterculia lanceolata, a Celtis sinensis, a Tabebuia chrysantha and a Cinnamomum camphora. Results suggest that broadleaved trees might exhibit vibration in a wide frequency band, whereas the coniferous trees could follow a distinct dominant frequency.

Influence of Plants on the Spatial Variability of Soil Penetration Resistance

Soil penetration resistance is an informative indicator to monitor soil compaction, which affects a range of ecological processes in floodplain ecosystems. The aim of the investigation was to reveal the influence of vegetation cover on the spatial variability of penetration resistance of floodplain soils. The study was carried out in the elm oak forest in the floodplain of the Dnipro River (Dniprovsko-Orilsky Nature Reserve, Ukraine). The study of the soil profile morphology was performed in accordance with the guidelines of the field description of soils FAO. The soil penetration resistance was measured in the field using the Eijkelkamp manual penetrometer to a depth of 100 cm at 5-cm intervals within the polygon consisted of 105 sampling points. Vegetation descriptions were made in a 3×3-meter surrounding from each sampling point. The soil penetration resistance was found to regularly increase with increasing depth. The changes in resistance values were insignificant until 25–30 cm depth. After that, there was a sharp increase in penetration resistance up to the depth of 70–75 cm, after which the indicators plateaued. In the three-dimensional aspect, the spatial variation of soil penetration resistance can be fractionated into broad-scale, medium-scale, and fine-scale components. Tree vegetation induces a broad-scale component of soil penetration resistance variations, which embraces the whole soil profile. The herbaceous vegetation induces a medium-scale component, which embraces the upper and middle parts of the soil profile. The fine-scale component is influenced by pedogenic factors.

Plant vibrations at all scales: a review

Plant vibrations is a wide subject that covers topics ranging from the swaying of trees under wind to elastic waves made by an insect on a leaf to communicate with its neighbors. For this reason, the state of the art is somehow fragmented over several communities. This review aims at giving a general overview of the main results and challenges in plant vibrations. Several scales are considered, from the very small and local, in leaves or fruits, to large canopies of many plants.