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空间任意运动曲梁的问题目前已有文献研究,所用方法可分为两类:1.经典的方法,适于简单梁如旋转直梁等;2.有限元等数值计算方法,适于空间任意曲梁,但需要较为复杂的单元分析.本文试图采用兼有二者特点的方法,即根据经典力学的简单公式,得到了由于大位移运动作用于系统的惯性力,再利用静止曲梁的刚度与质量矩阵等,得到了系统的运动方程.文中以旋转直梁的固有频率计算为例,得到了与有关文献十分接近的结果,证明了方法的正确性.
At present, there are literature studies on the curved beams with arbitrary motion. The methods used can be divided into two categories: 1. The classical method is suitable for simple beams such as rotating straight beams, etc. 2. Numerical calculation methods such as finite element are suitable for any space However, it requires more complicated unit analysis.This paper attempts to adopt a method that combines the characteristics of the two, that is, according to the simple formula of classical mechanics, the inertial force acting on the system due to the large displacement motion is obtained, and the stiffness of the static bending beam And the mass matrix, we get the equations of motion of the system.In this paper, the calculation of the natural frequency of rotating straight beam is taken as an example, and the result is very close to that of the related literatures, which proves the correctness of the method.