惯性边界下梁的非线性振动分析

摘要

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.%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。