大范围转动弹性梁非线性动力学建模与摄动解耦

Non-linear dynamic modeling and perturbation decoupling of the elastic beam in large overall rotation

计及弹性梁大范围转动与弹性小变形之间的耦合作用,应用假设模态法进行坐标离散,采用Galerkin法和Hamilton原理建立弹性梁刚柔耦合非线性动力学模型;依据摄动理论构建正则摄动式,进而完成弹性梁非线性动力学的摄动解耦,在此基础上深入解析了摄动解耦误差及有效时间序列与阻尼系数的耦合关系。研究结果表明:在有效时间序列内摄动解耦精度较高,可通过简单增加摄动级数来进一步提高精度,避免了数值类方法存在的大量计算。

In this article,the method of assumed modes is adopted to discrete the coordinates,and both the Galerkin method and the Hamilton principle are employed to work out the non-linear dynamic model of the elastic beam,with the coupling effect between large overall rotation and elastic deformation taken into account.The regular perturbation formula is deduced based on the perturbation theory,in order to complete the perturbation decoupling of non-linear dynamics.The analysis is conducted on both the error of perturbation decoupling and the distribution characteristics of effective time series.It is shown that a higher standard of perturbation decoupling is ensured during the effective time series.Also,accuracy can be improved by increasing the perturbation solution according to the practical requirements,which avoids much calculation by means of the numerical method.