含有初始弯曲的功能梯度输流管的平衡分岔分析

Equilibrium bifurcation analysis of functionally graded pipe conveying fluid with initial curvature

在现实生活中,管道几乎都是含有初始弯曲的。针对这一现象,解析研究了含有初始弯曲的功能梯度输流管的平衡分岔问题。基于欧拉-伯努利梁理论和广义哈密顿原理,推导了固支边界条件下含有初始弯曲的功能梯度输流管的纵横耦合非线性振动方程。对建立的非线性方程进行解析求解,给出了超临界流速下直管和含初始弯曲的功能梯度输流管平衡位形和临界流速的解析表达式。分析了幂律指数、管道长度以及初始弯曲幅值等参数对系统平衡分岔的影响,并对直流管系统和含有初始弯曲的输流管系统的临界流速进行了对比分析。

In real life,almost all pipes contain initial curvature.Here,aiming at this phenomenon,equilibrium bifurcation of functionally graded pipe conveying fluid with initial curvature was analytically studied.Based on Euler-Bernoulli beam theory and the generalized Hamiltonian principle,longitudinal-transverse coupled nonlinear vibration equations of a functionally graded pipe conveying fluid with initial curvature under fixed boundary conditions were derived.The nonlinear equations were solved analytically,and analytical expressions for equilibrium configurations and critical flow velocities of functionally graded straight pipe and functionally graded pipe with initial curvature under supercritical flow velocity were obtained.Effects of power-law exponent,pipe length and initial curvature amplitude on equilibrium bifurcation of the system were analyzed.Critical flow velocities of straight pipe conveying fluid system and pipe conveying fluid system with initial curvature were analyzed contrastively.