惯性边界下带钢的非线性振动分析

根据连轧机轧制过程中带钢与轧辊的运动机理，将相邻两机架间的带钢简化为轴向运动的Euler梁，轧辊简化为定轴转动的惯性元件，建立Euler梁在惯性边界下的非线性振动力学模型。基于哈密顿原理建立轴向运动Euler梁的纵向和横向非线性振动微分方程，利用Kantorovich时间平均法简化运动方程和边界条件，并采用修正迭代法求解运动方程。最后通过数值计算获得了Euler梁非线性振动的幅频响应曲线，并讨论惯性边界条件下的轴向运动速度、长度和轧辊的转动惯量对Euler梁振动特性的影响。研究结果可为控制和分析连轧过程中带钢垂直振动提供重要的理论参考。

Analysis of Nonlinear Vibration of Strip with Inertial Boundary Conditions

According to the movement mechanism of strip and rollers in the rolling process of tandem mill, the strip between stands was simplified to axially moving Euler beam and the rollers were simplified to the inertia component on the fixed axis rotation, namely inertial boundary conditions. Nonlinear vibration mechanical model of the Euler beam with inertial boundary conditions was established. The longitudinal and lateral motion equations of the Euler beam were derived due to the Hamilton's principle. The Kantorovich averaging method was used to simplify the motion equations and the inertial boundary, and the modified iteration method was employed to solve the motion equations. Finally, based on the results of numerical analysis, the amplitude frequency response curves of the Euler beam were obtained, and the influence of the axial velocity, the length and the rotational inertia of the roller on the vibration performance of Euler beam on condition of inertial boundary. The results may provide an important theoretical reference to control and analyze the vertical vibration of strip in the continuous rolling process.