基于广义传递函数的非线性碰撞数据模态分析

秦真山¹，陆史浩¹，阮军武¹，李思远^2*，宋汉文^3*

1.广西玉柴机器股份有限公司工程研究院，广西 玉林  537000；

2.山东大学能源与动力工程学院，山东 济南  250061；

3.同济大学航空航天与力学学院，上海  200092

摘要：研究机械系统各部件间隙导致的碰撞现象，设计单边约束悬臂梁施加正弦激励的碰撞试验，根据实测的悬臂梁各离散点加速度响应与碰撞力构造广义传递函数，仿真分析混沌响应和周期响应下该广义传递函数的模态分布。结果表明：混沌响应下的传递函数包含准确的模态频率信息，且该广义传递函数与系统所受水平激励的振幅无关；将仿照ERA-NExT法辨识出的模态参数与悬臂梁模态振型进行比较，发现由混沌响应得到的模态振型与悬臂梁模型的模态振型整体一致，前4阶振型的吻合程度很好。

关键词：非线性振动；悬臂梁；单边碰撞；混沌运动；模态辨识

Modal analysis of nonlinear collision data based on generalized transfer function

QIN Zhenshan¹, LU Shihao¹, RUAN Junwu¹, LI Siyuan^2*, SONG Hanwen^3*

1.Engineering R&D Institute, Guangxi Yuchai Machinery Co., Ltd., Yulin 537000, China;

2.School of Energy and Power Engineering, Shandong University, Jinan 250061, China;

3.School of Aerospace Engineering and Applied  Mechanics, Tongji University, Shanghai 200092,China

Abstract：In order to investigate the collision phenomenon caused by the gap between various parts of the mechanical system, a collision test with sinusoidal excitation is designed for an unilaterally constrained cantilever beam. The generalized transfer function is constructed based on the measured acceleration response of each discrete point of the cantilever beam and the collision internal force. Meanwhile, the modal distributions of the generalized transfer function under chaotic response and cyclic response are analyzed by simulation. The results show that the transfer function under chaotic response contains accurate modal frequency information, and this generalized transfer function is independent of the amplitude of the horizontal excitation to the system. Comparing the identified modal parameters modeled after the ERA-NExT method with the cantilever beam modal shapes, it is found that the modal shapes obtained from the chaotic response are in overall consistency with those of the cantilever beam model, and the first four orders of the modal shapes are in good accordance with each other.

Keywords: nonlinear vibration; cantilever beam; unilateral collision; chaotic motion; modal identification