A Numerical Approach to Estimate Natural Frequency of Trees with Variable Properties

Abstract

Free vibration analysis of a Euler-Bernoulli tapered column was conducted using the finite element method to identify the vibration modes of an equivalent tree structure under a specified set of conditions. A non-prismatic elastic circular column of height L was analysed, taking distributed self-weight into account. Various scenarios were considered: column taper, base fixity, radial and longitudinal stiffness (E) and density (ρ) and crown mass. The effect on the first natural frequency was assessed in each case. Validation against closed form solutions of benchmark problems was conducted satisfactorily. The results show that column taper, base fixity and E/ρ ratio are particularly important for this problem. Comparison of predictions with field observations of natural sway frequency for almost 700 coniferous and broadleaved trees from the published literature showed that the model worked well for coniferous trees, but less well for broadleaved trees with their more complicated crown architecture. Overall, the current study provides an in-depth numerical investigation of material properties, geometric properties and boundary conditions to create further understanding of vibration behaviour in trees.

Quantification of One-Year Gypsy Moth Defoliation Extent in Wonju, Korea, Using Landsat Satellite Images

“…Our results showed that remote sensing methods are useful for detecting or monitoring damage caused by some forest pests, such as those that occasionally reach outbreak densities or that are newly invasive species. Moreover, the defoliation maps estimated by remote sensing techniques can be basic information for outbreak risk analysis using numerical and mathematical methods [26][27][28][29][30].…”

Challenges and Capabilities in Estimating Snow Mass Intercepted in Conifer Canopies With Tree Sway Monitoring

“…When subject to a wind gust, a coniferous tree sways in a manner characteristic of a damped harmonic oscillator, for example, a vertical cantilever beam (Figure 3d) (Blevins, 1979; Bunce et al., 2019; Dargahi et al., 2020; Gardiner, 1992; T. Jackson et al., 2019; Moore & Maguire, 2004; Peltola, 1996; Pivato et al., 2014). In this approximation, the natural sway frequency ( f , Hz) depends on its mechanical, geometric, and mass properties, and is conceptualized as (Blevins, 1979): $$$f\propto \frac{1}{2\pi }\sqrt{\frac{K}{m}}$$$ where K is the flexural rigidity (or stiffness) and m is the total mass (kg) of the tree, including biomass and canopy water storage.…”

“…When subject to a wind gust, a coniferous tree sways in a manner characteristic of a damped harmonic oscillator, for example, a vertical cantilever beam (Figure 3d) (Blevins, 1979;Bunce et al, 2019;Dargahi et al, 2020;Gardiner, 1992;T. Jackson et al, 2019;Moore & Maguire, 2004;Peltola, 1996;Pivato et al, 2014).…”

Simulation of Heat and Water Transport on Different Tree Canopies: A Finite Element Approach

“…This allows the formulation of different models, single or multi-layered, to study the different phenomena in forest and plants canopies, some of which are harmful to human life quality. Several examples could be enunciated: an evaluation of the radiation that reaches the soil and tree transpiration as means to mitigate the urban heat island (UHI) [2], a study of trees resistance to wind loads, and efficiency evaluation of trees as windbreakers [3], formulation of a multi-layer model to estimate the radiation distribution inside the canopy [4], use of a high-resolution model to study the water stress in a forest mulch layering [5], estimation of heat and water fluxes in the soil layer [6].…”