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Open AccessArticle

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

1
Department of Civil and Environmental Engineering, Western University, London, ON N6A 5B9, Canada
2
Timberlands Limited, Rotorua 3040, New Zealand
*
Author to whom correspondence should be addressed.
Forests 2020, 11(9), 915; https://doi.org/10.3390/f11090915
Received: 3 July 2020 / Revised: 13 August 2020 / Accepted: 18 August 2020 / Published: 21 August 2020
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. View Full-Text
Keywords: tree; natural frequency; non-prismatic; elastic modulus; density; crown mass tree; natural frequency; non-prismatic; elastic modulus; density; crown mass
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MDPI and ACS Style

Dargahi, M.; Newson, T.; R. Moore, J. A Numerical Approach to Estimate Natural Frequency of Trees with Variable Properties. Forests 2020, 11, 915.

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