梁纵横耦合振动研究

Studies on the Longitudinal and Lateral Coupled Vibration of Beam

针对梁纵横耦合振动的非线性运动问题,导出了适用于求解该问题的梁单元非线性刚度矩阵,并提出了相应的具有通用性的有限元解法,可推广到复杂结构求解.通过实例数值计算,分析了梁纵横振动的耦合效应机理,研究表明耦合振动的频率成分是激励频率以及固有频率的加减组合和倍频的结论,因此结构设计时除了考虑使系统的固有频率避开激励频率外,还应考虑避开激励频率组合值.

On the basis of other scholars＇ work,the non-linear motion equations about the longitudinal and lateral coupled vibration of beam are proposed firstly.Then,in order to solve this problem,the beam element＇s non-linear stiffness matrix,which is suitable for solving the coupled problem,is educed and the relevant finite elements method is presented in this paper.Finally,a practical calculation example is calculated numerically by this method and the coupling mechanism of the beam＇s longitudinal and lateral vibration is analyzed in detail.On the basis of the analysis,the conclusion is that the frequencies of the coupled response are the combination of the exciting frequencies and the natural frequencies of the system,so the natural frequencies of the structure should avoid the combined frequencies of the exciting frequencies except them,which has a directive meaning for practical engineering problems.