Effects of clamping angle of a vibration shaker on vibration energy transfer in tree branches for walnut mechanical harvesting

In current walnut vibration harvesting operations, lateral-branch clamping is still frequently performed or adjusted manually, and perfectly orthogonal clamping is difficult to maintain because of irregular branch orientations, limited operating space, and machine posture deviations. To address the issues of inefficient energy transfer and tree damage caused by non-standard clamping of lateral branches in unstructured environments, this study proposes a continuum dynamics model based on the generalized force concept. This model aims to analyze the influence of excitation force vector direction on the vibration transfer mechanism of dual-axis and triple-axis branched walnut trees. An analytical solution for forced vibration incorporating angular parameters was derived based on Euler-Bernoulli beam theory. The theory indicates that the lateral acceleration response is proportional to the sine of the clamping angle α. The model's validity in both frequency and time domains was validated through multi-condition comparisons between finite element simulations and field experiments. Results indicate that energy transfer efficiency at terminal branches peaks when the excitation force vector is orthogonal to the branch axis. As the angle deviates from orthogonality, acceleration responses at key measurement points significantly attenuate. Additionally, the tree's topological structure exhibits a modulation effect on wave propagation, with branching nodes showing pronounced local amplitude attenuation due to mass accumulation. Under the operational conditions, tree samples, excitation frequency, and clamping device configuration used in this study, when the clamping angle α shifted from 90°to 95°, the acceleration signal energy decreased by approximately 21.36%. This lost effective vibration signal energy may have been mainly converted into axial work or dissipated at the bark–clamp contact interface, thereby increasing the risk of bark tearing. These findings clarify the relationship between clamping posture and vibration response, providing guidance for precision clamping in low-damage walnut harvesting.