# Dynamic response of Blue Honeysuckle fruit-stem system based on mathematical model

## TL;DR

This study models how Blue Honeysuckle fruits detach during vibratory harvesting, helping improve mechanical harvesting techniques for berry crops.

## Contribution

A novel dynamic model of the fruit-stem system under vibratory excitation is developed and validated with experiments.

## Key findings

- Fruit detachment occurs when stem stress exceeds allowable limits under low-frequency excitation.
- Vibrational instability causes detachment when the fruit stem is aligned parallel to the excitation direction.
- Theoretical predictions match experimental results, confirming the model's accuracy.

## Abstract

To investigate the motion and detachment behavior of Blue Honeysuckle fruit during vibratory harvesting, the fruit-bearing branch was modeled as a constant strength beam, and an analytical series solution for its dynamic response was derived. This solution shows that the branch undergoes approximately simple harmonic motion under low frequency excitation. Subsequently, a dynamic model of the fruit-stem system subject to branch oscillation with the fruit stem at an angle to the excitation direction was developed. When the fruit stem is perpendicular to the excitation direction, the stress within it can exceed its allowable limit under low frequency excitation, leading to fruit detachment. Conversely, when the fruit stem is aligned parallel to the excitation direction, fruit detachment results from the vibrational instability of the fruit-stem system. For the case where a small angle exists between the stem and the excitation direction, the criterion for vibrational instability remains consistent with that of the parallel scenario. Modal analysis and frequency sweep analysis were performed using the finite element method (FEM) to study the vibration response characteristics of the fruit-stem system. The finite element simulation results are in close agreement with theoretical calculations. Field vibration experiments were carried out in an experimental plot. The experimental data confirmed that the simplified dynamic model can accurately predict the fruit detachment patterns. The findings of this study can serve as a theoretical foundation for the design, selection, and optimization of mechanical harvesting equipment for berry crops.