Modal frequency analysis for Camellia oleifera with sympodial branching growth mode using allometric scaling law

Abstract

In this paper, the branching growth mode of Camellia oleifera is considered to be a sympodial branching pattern. A simplified fractal model of Camellia oleifera is established with several similar basic units. The morphological parameters of the basic bifurcated units in the tree model are correlated according to the biological allometric scaling law. For the basic bifurcated unit, a cantilever trunk modelled as the Euler-Bernoulli beam with two lateral branches is obtained regardless of the mass of foliage. The modal frequency of the basic bifurcated unit is calculated using Hamilton's principle. Finite element simulation using ANSYS software is performed to obtain the simulation modal frequencies in comparison with the theoretical frequencies. An empirical formula relating to the modal frequencies is derived from the perspective of energy transfer. The effect of branch angle on the modal frequency is further investigated. Besides, the empirical formula is extended for the calculation of the modal frequency of three basic bifurcated units. The modal frequency in branch mode is also obtained and compared with the simulation results. In the field measurement, two coefficients involving the lateral branching ratio and the slenderness coefficient were identified from the morphological measurements. The modal frequency for the basic bifurcated unit and the tree were measured using the dynamic signal analyser. The relative errors of the modal frequency from the empirical formulas and the field experiments are less than 6 %, which demonstrates the feasibility of the modal frequency analysis of Camellia oleifera using the proposed empirical formulas.