拉格朗日键合图的欧拉梁的模态分析

研究了利用拉格朗日键合图建立梁横向振动数学模型的基本方法.由于拉格朗日键合图方法中能量转换矩阵对广义坐标的要求,将梁离散为刚杆-质点-弹簧系统,定义挠度为广义坐标,然后分析了多种边界条件下梁横向振动的数学模型.最后以两端简支梁为例作了仿真计算,其仿真结果与该模型的理论解以及ANSYS的计算结果进行了对比,验证了梁的离散模型的有效性,并说明了拉格朗日键合图对梁横向振动进行模态分析相对于别的方法是简便可行的.

Modal analysis of Euler beam based on Lagrangian bond graph

The basic method to establish a mathematical model of bending vibration of Euler beam using Lagrangian bond graph is studied in this paper.Out of the request for the generalized coordinates from energy transformation matrix in Lagrangian bond graph method,Euler beam will be discretized into a rigid bar-massspring model.Only generalized deflection variable is defined.And the mathematical model of bending vibration is deduced under various boundary conditions.Simulation on a beam with both ends simply pivoted is carried out,and the results are compared with the theoretical analysis and the results of finite element method,which proves that the discrete model of the beam is effective and accurate,and modeling by use of Lagrangian bond graph is feasible.