基于物理杆的多级Y型银杏树动力学建模及试验

Kinetic modeling and experiment of multistage Y shaped ginkgo tree based on physical rod

研究果树个体的动力学特性有利于提升果实振动采收的基础理论,果树动力学特性可通过动力学建模和实验分析两种手段获得。基于等截面和变截面物理杆模型对多级Y型银杏树进行了建模研究,通过微分方程的求解并与测试结果进行了对比分析验证。结果表明:实测频谱曲线上低于15.00 Hz的低频区,主干与各级侧枝出现了较明显的波峰,且各阶频率值较一致;高于15.00 Hz的高频区,各枝干的频谱曲线一致度较差,具有各自不同的波峰特征及对应的谐频点。果树的主干和分枝之间存在一定的运动独立性,基于物理杆模型计算条件下,果树的主干只能激发出基频。受到模型自由度的限制,果树只能激发出和系统自由度相同个数的谐振频率,且只能激发出低阶频率。变截面物理杆模型与等截面物理杆模型相比,不仅在一级侧枝上就能激发出全部的5阶谐振频率点,而且模型的计算精度远高于等截面物理杆模型,说明变截面物理杆模型更加接近于果树实际的形态结构,更能准确地体现出果树的频谱特性。因此,通过数学建模方法只能激发出有限个低频区的谐振频率,要想获得更多阶的谐振频率及更宽的频率范围,需通过增加更多分枝形成更多自由度的方法才可获得。

Studying the dynamic characteristics of individual fruit tree is beneficial to improve the basic theory of fruit vibration harvesting.The dynamic characteristics of the fruit tree could be obtained by dynamic modeling and experimental analysis.Based on the equal and variable cross section physical rod models,the model of a multistage Y-type ginkgo tree was established in this paper.The differential equation was solved and compared with the results from the experiment.The results showed that on the measured spectrum curve,in the low frequency region(below 15.00 Hz),the trunk and branches presented obvious peaks and the frequency values of different orders were consistent.In the high frequency region(above 15.00 Hz),the spectral curves of branches presented poor consistency,with different peak characteristics and corresponding harmonic points.There was a certain degree of motion independence between the trunk and branches of the fruit tree.Under the condition of the physical rod model,only the fundamental frequency could be stimulated on the trunk.Limited by the degree of freedom of the model,only the same number of resonant frequencies as the degree of system freedom could be excited by the fruit tree.Furthermore,all the resonant frequencies were low-order frequencies.Compared with the equal cross section physical rod model,the variable-section physical rod model could stimulate all the five-order resonant frequency points on the first-stage side branches.What s more,the calculation accuracy of the model was much higher than that of the equal cross section physical rod model.It was indicated that the variable cross section physical rod model was closer to the actual morphological structure of the fruit tree and could more accurately reflect the spectral characteristics of the fruit tree.Therefore,only the resonant frequency with finite number in low frequency region could be excited by the method of mathematical modeling.Only by adding more branches to form more degrees of freedom,more resonant frequencies and wider frequency range could be obtained.