Galerkin截断方法在轴向运动梁问题中的应用

The method of Galerkin truncation on the vibration of axially moving beams

研究了Galerkin截断方法在不同支承条件下轴向运动梁振动问题中的应用.利用离散化后的微分方程在u—vf平面上的失稳区域随离散维数的变化情况,验证了两端铰支的轴向运动梁取正弦函数做Galerkin截断方法时所得结果的正确性,对于两端固支的轴向运动梁,选取不同的特征函数,分别应用Galerkin截断方法并比较所得结果,最后得到适用于此种支承条件下的离散方法.

In this paper, the stabilities of axially moving beams are investigated. The n - term Galerkin truncations are employed to simplify the partial - differential equations that govern the transverse motion of beams into a set of ordinary differential equations. Simple supported and fixed beams are considered respectively. Given different truncation term n, the instability regions on the u-vf map are contrasted to each other. Adopting the right eigenfunctions, it was found 3 - term truncation is almost accurate. For simple supported beam, taking sine series as the eigenfunctions turns out effective results. And for the fixed beam, two type of eigenfunctions are considered and then the best one is selected by studying the instabilities of the truncated system.