Vibration response of blue honeysuckle branches based on mathematical model

For vibratory harvesting of blue honeysuckle, excitation must generate sufficient inertial force to detach the fruit, but the vibration energy is always absorbed by the trunk and root system, which decreases the inertial force. This study investigated the vibration response of fruit branches under excitation to achieve efficient harvesting. A simplified Y‑shaped branch model was established, and then dynamic equations of this branch system were derived. Based on branch angle characteristics, the dynamic equations were simplified. When the angle between a branch axis direction and the excitation direction is small, a specific excitation frequency induces parametric resonance in the branch system, leading to unstable vibration of the branch system. Under weak coupling conditions, the relationship among excitation amplitude, frequency, and geometric parameters of the branch that produce unstable vibration was derived, and the influence of variations in branch geometric parameters on the instability region was found. By establishing a finite element model of the branch system, the natural frequencies were calculated, and vibration amplitudes under different excitation frequencies were obtained through numerical simulation, which clarified the response characteristics of the branch during parametric resonance. To verify the theoretical and finite element analyses, branch vibration experiments were conducted. The maximum vibration amplitude of the branch under different excitation frequencies was measured, and the parametric resonance behavior was analyzed accordingly. The finite element calculations and experimental results agreed well with the theoretical model predictions, indicating that the theoretical model can provide a reliable basis for the design of vibratory harvesting machinery for blue honeysuckle.