CAJ | 학술논문

本文基于轧制过程中轧辊与带材的振动，将带材简化为Euler梁，轧辊简化成惯性元件，建立了梁在惯性边界下的非线性振动模型，首先根据哈密顿原理建立梁的纵向和横向非线性振动微分方程和惯性边界条件，再利用Kantorovich平均法简化运动方程和边界条件，然后采用修正迭代法求解方程。通过数值计算获得了梁的幅频响应曲线，研究了梁振动的非线性性态的变化规律，并讨论了惯性边界条件下梁的长度、惯性元件的转动惯量对梁的振动频率的影响规律。
본문기우알제과정중알곤여대재적진동，장대재간화위Euler량，알곤간화성관성원건，건립료량재관성변계하적비선성진동모형，수선근거합밀돈원리건립량적종향화횡향비선성진동미분방정화관성변계조건，재이용Kantorovich평균법간화운동방정화변계조건，연후채용수정질대법구해방정。통과수치계산획득료량적폭빈향응곡선，연구료량진동적비선성성태적변화규률，병토론료관성변계조건하량적장도、관성원건적전동관량대량적진동빈솔적영향규률。
Based on the vibration of steel rolls and the strip in the process of rolling, the strip is simplified to Euler beam, the rolls are simplified to inertia components. Firstly, the longitudinal and lateral motion equations of a beam is derived by Hamilton's prin-ciple, the inertial boundary is established. Then the Kantorovich method is used to reduce the motion equations. Finally, the modified iteration method is employed to solve the nonlinear vibration equations. According to the results of numerical analysis, the amplitude frequency response curves of the beams are obtained, and the change rule of nonlinear behavior is studied, the rela-tionships between the vibration frequency of the beam with inertial boundary conditions and the length of the beam or the rotational inertia of the inertia components are discussed.