Finite Element and Applied Models of the Stem with Spike Deformation

Abstract

This article examines the static and dynamic deformation of the stem of an ear of wheat and of the individual grain. The purpose of the article is to determine the factors of influence on the ear of wheat to isolate the grain. Two stages of grain ripening are considered: in the early stage, the grain is attached to the spike by the stem; in the second, there is no stem, and the grain is attached to the ear by the scales. The ear fluctuations are considered within the Euler–Bernoulli bar theory. The developed model divides the study of the dynamics of the stem of an ear and the dynamics of the grain into two stages. The first stage studies the dynamics of the plant as a whole, while the second stage studies the dynamics of an individual grain in a moving system associated with the ear in bending and vertical fluctuation forms. The model of the ear and the grain fluctuation uses the mechanical characteristics of elastic bonds and elastic bodies, which are determined by spring stiffness, elastic moduli, etc. The results show that in the vertical forms of grain fluctuation, the frequency of fluctuation is much higher than in the bending ones. This article presents the natural fluctuation frequencies of grain at full ripeness and in the early phases of maturation, at which point it is released from the ear.

Keywords

• harvest
• grain of wheat
• ear of grain
• mathematical model
• early stages of maturation
• ear fluctuations