钻柱横向非线性振动分析

利用同伦分析法求解了钻柱横向非线性振动方程,得到了该非线性振动的频率和主振动的一阶近似解析解.分析过程中发现,同伦分析法在求解钻柱横向非线性振动方程时不需要引入以往摄动求解的小参数,这样提高了近似解的精度和扩大了解的适用范围.计算结果表明非线性因素改变了主振动的形态,使其不再成为简谐振动,同时非线性因素对频率的影响程度随着振幅、轴向压力和钻柱长度的增大而增加.因此,对于受较大轴向压力作用的长钻柱横向振动,应当考虑非线性因素的影响.

Analysis on transverse nonlinear vibration for drilling shafts

By using the homotopic analysis method to solve the transverse nonlinear vibration equation,the nonlinear vibration frequency,together with the first order approximate analytic solution of preliminary vibration,is obtained.Pertaining to the homotopic analysis method,the minor parameters for previously-applied perturbation solution are not introduced.In this way,the approximate solution accuracy and adaptation range are enhanced.To this end,it is found from computational results that the nonlinear factors ch...