基于直曲组集算法的复杂液压管路固有频率分析

Natural frequency analysis of complex hydraulic pipelines based on straight-curved pipeline assembly algorithm

航空管路系统布局形式复杂多变,如"L"形管路、"U"形管路、"Z"形管路等,这些管路布局中均包含"直管—曲管"这一典型管道基本元件。对此,提出"直管—曲管"组集(直曲组集)算法,实现复杂管路的高效建模和模态分析;分别从直管单元与曲管单元的三维振动控制方程出发,基于频散关系,推导了管道单元自由振动的离散模式和动力刚度矩阵;然后在全局坐标系下实现直曲组集,建立了管路系统动力刚度矩阵和特征方程;最后,对所提算法进行了验证,并采用该法分析了管路布局对"Z"形管固有频率的影响规律,建立了经验公式。通过试验发现,公式与试验结果基本相符,对比误差<5%,说明在误差许可范围内,所拟公式可用于"Z"形管设计。

The geometry of air pipeline system is generally complicated,such as,L-shaped,U-shaped,Z-shaped configurations and so on,but they contain a typical pipeline basic element of“straight pipe-curved pipe”.Here,an algorithm based on straight-curved assembly pipeline was proposed to realize more efficient modeling and modal analysis of complex pipeline systems.Starting from 3-D vibration governing equations of a straight pipe element and a curved one,respectively,discrete modes and dynamic stiffness matrices of pipe elements were derived based on frequency dispersion relation.Then all straight pipe elements and curved ones were assembled under a global coordinate system,the whole pipeline system’s dynamic stiffness matrix and characteristic equation were established.Finally,the proposed algorithm was validated.This method was used to analyze the influence law of piping layout on natural frequencies of Z-shaped pipes and deduce the empirical formula.Tests showed that the results of the empirical formula agree well with those of tests,their error is less than 5%,so the empirical formula can be used to design Z-shaped pipes within an allowable error range.