基于同伦分析法的FGM输流管非线性频率分析  

Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method

作　　者：周杰 常学平[1] 李映辉[2] 邵永波[3] ZHOU Jie;CHANG Xueping;LI Yinghui;SHAO Yongbo(School of Mechatronic Engineering,Southwest Petroleum University,Chengdu 610500,P.R.China;School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu 610031,P.R.China;School of Civil Engineering and Geomatics,Southwest Petroleum University,Chengdu 610500,P.R.China)

机构地区：[1]西南石油大学机电工程学院,成都610500 [2]西南交通大学力学与航空航天学院,成都610031 [3]西南石油大学土木工程与测绘学院,成都610500

出　　处：《应用数学和力学》2023年第2期191-200,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51674216)。

摘　　要：该文基于同伦分析法研究了广义边界条件下含孔隙功能梯度材料(FGM)输流管道的非线性振动.基于FGM的幂律分布规律和Voigt模型来描述具有孔隙的FGM管道的材料特性.基于Euler-Bernoulli梁理论和von Kármán非线性理论,利用Hamilton变分原理,建立了含孔隙功能梯度流体输送管道的动力学控制方程和广义边界条件.采用同伦分析法求解了广义边界条件下的功能梯度流管道的非线性振动特性.数值结果表明:平移弹簧对失稳的临界流速影响不明显,而扭转弹簧则提高了失稳的临界流速,使系统更加稳定;在非线性系统中,黏弹性系数不会改变失稳临界流速;管道长度、幂律指数和孔隙率都会对FGM多孔输流管道的非线性自由振动有明显的影响.Based on the homotopy analysis method,the nonlinear vibration of porous functionally graded material(FGM)conveying pipes under generalized boundary conditions was studied.Based on the power-law distribution of the FGM and the Voigt model,the physical properties of the porous pipe material were described.Under the Euler-Bernoulli beam theory and the von Kármán nonlinear theory,and by means of Hamilton’s variational principle,the dynamic control equations and generalized boundary conditions for porous FGM conveying pipes were established.The homotopy analysis method was used to solve the nonlinear vibration characteristics of the porous FGM conveying pipe under generalized boundary conditions.The numerical results show that,the translation spring has little effect on the critical velocity of instability,while the rotation spring increases the critical velocity of instability,making the system more stable;in the nonlinear system,the viscoelastic coefficient does not change the critical velocity;the pipe length,the power-law exponent and the porosity all influence the nonlinear free vibration of the porous FGM conveying pipe.

关 键 词：同伦分析法 广义边界条件 非线性振动 孔隙率 输流管道 

分 类 号：O322[理学—一般力学与力学基础]