用Newmark法求解旋转细长梁的影响因素分析

Analysis of effects about the solution to revolving slightness beam with Newmark method

采用Newmark法求解旋转细长梁问题 ,分析了时间步长、积分常数和直径与杆长比 3个因素的影响 .算例表明 :计算时间步长选择 2～ 10 (°)较为合理 ,能够在保证计算精度的同时 ,提高计算效率 ;积分常数选取值愈大 ,转矩振幅衰减愈快 ,当积分常数取 3 .5 0时 ,旋转杆件能够在 2个周期内趋于稳定 ;直径与杆长之比大于 1∶10 4 时 ,杆件的上、下两端角位移出现明显差异 ,表现出细长杆的旋转特性 .这 3个因素的影响规律与理论分析结论相一致 ,为工程应用提供了计算依据 .

The method of Newmark is adopted to solve the problem of revolving slightness beam, and it can analyse the three effectstime step, integration parameters and the ratio of diameter and length. It is proved by calculated example :It is rational that calculated time step adopts 2～10(°), because it not only ensures the accuracy of the solution, but also improve calculating efficiency; the bigger the integration constants, the faster that attenuation of revolving moment wings. When integration parameters is 3.5, revolving bar will be stabilized in two cycles; when the ratio of diameter and length is bigger than 1:10k, there are obvious difference in the angular displacement of the top and bottom point of bar, showing the revolving property of slightness bar. The theory analysis is consistent with the influence rules of the three factors, and provides the basis of calculation for engineering application.