模态方法下的悬臂梁/类悬臂梁弹性构件的动力学建模

针对扁簧式起落架这一类悬臂梁弹性结构的弹性变形,提出了一种克服传统模态方法计算精度受限的模态旋转方法。首先,基于有限元理论中的小变形运动学分析推导出变形中旋转部分的表述方法。然后,总结了传统线性模态理论,提出了一种将旋转变形引入到模态坐标下动力学方程的方法,从而在结构动力学分析中引入旋转变形的影响,使模态方法适用于旋转变形较大的情况。最后,进行了扁簧式起落架静力学仿真及实验的对比验证。结果显示:在设计载荷100kg范围内,两种模态方法都能保证5%以内的计算精度;但在极限载荷180kg情况下,线性模态方法产生了超过35%的计算误差,而模态旋转方法仍能够保证10%以内的计算精度。仿真过程中两种模态方法的计算步长均为1ms。结果表明:与传统的模态方法相比,提出的模态旋转方法在相对旋转变形较大的情况下有更高的计算精度,同时保留了传统模态方法计算效率高的优点。

Modal method based dynamic analysis of cantilever type elastic structures

For the elastic deformation of cantilever type elastic structures in a flat spring landing gear, a new modal warp method was proposed to improve the calculation precision of the traditional modal method. Firstly, the description of a rotational component in infinitesimal deformation was deduced based on the finite element theory. Then the general modal method was summarized and how to introduce the rotational deformation into the dynamic equation in a modal coordinate was proposed. By which, the rotational deformation was introduced into the analysis of structure dynamics, so that the modal method could simulate the large bending and/or twisting deformation. Finally, the static simulation and experiments were performed and compared on the flat spring landing gear. The analysis results show that when the load mass is less than 100 kg, the relative errors are below 5% for both the linear modal method and modal warping method. However, when the load reaches to 180 kg(which represents the maximum realistic condition for landing), the error of the modal warp method remains within 10% and the error of linear modal has been more than 35%. Moreover, the time steps of both modal methods are 1 ms. As comparied with the traditional method, the modal warping method provides higher calculation and efficiency in the simulation of large rotational deformation.