Pipeline systems in aircraft are connected to the airframe through numerous clamps. There are multiple excitation points and the excitation frequency range is wide, being influenced by accessories such as valves and flanges. To analyse this situation, the method of reverberation ray matrix (MRRM) is extended by random vibration theory to the steady-state random response analysis of a three-dimensional multi-span hydraulic pipeline under multi-point base excitations. Advantages of this approach are that less computational effort is required, cross-correlations between excitations are automatically included, and each response of the system has an exact and unified solution scheme. Each span is represented by the Timoshenko beam model, considering the influence of internal fluid, axial force and pressure of the pipeline, as well as clamps and accessories. An accurate steady-state wave solution for the displacement and internal force of the three-dimensional hydraulic pipeline is derived. The method utilises the analytical characteristics of MRRM and is not limited by the frequency range. Numerical examples demonstrate high accuracy and computational efficiency over a broad frequency range by comparison with random vibration analysis based on the finite element method for a section of hydraulic pipeline subjected to a wide range of random excitation. A systematic parametric study for the hydraulic pipeline system investigates the influences of various boundary conditions, fluid velocity and multi-point excitation coherence.

飞机中的管道系统通过多个夹具连接到机身。激励点多，激励频率范围宽，受阀门、法兰等附件影响。针对这种情况，利用随机振动理论将混响射线矩阵(MRRM)方法推广到多点基础激励下三维多跨液压管道的稳态随机响应分析。这种方法的优点是需要较少的计算工作，自动包含激励之间的互相关，并且系统的每个响应都有一个精确统一的解决方案。每个跨度用铁木辛哥梁模型表示，考虑管道内部流体、轴向力和压力的影响，以及夹子和配件。推导出三维液压管道位移和内力的精确稳态波解。该方法利用了MRRM的分析特性，不受频率范围的限制。数值算例通过与基于有限元方法的随机振动分析相比，在宽频率范围内具有较高的精度和计算效率，对一段受到广泛随机激励的液压管道进行了比较。液压管道系统的系统参数研究调查了各种边界条件、流体速度和多点激励相干性的影响。该方法利用了MRRM的分析特性，不受频率范围的限制。数值算例通过与基于有限元方法的随机振动分析相比，在较宽的频率范围内具有较高的精度和计算效率，对一段受到大范围随机激励的液压管道进行了比较。液压管道系统的系统参数研究调查了各种边界条件、流体速度和多点激励相干性的影响。该方法利用了MRRM的分析特性，不受频率范围的限制。数值算例通过与基于有限元方法的随机振动分析相比，在较宽的频率范围内具有较高的精度和计算效率，对一段受到大范围随机激励的液压管道进行了比较。液压管道系统的系统参数研究调查了各种边界条件、流体速度和多点激励相干性的影响。数值算例通过与基于有限元方法的随机振动分析相比，在较宽的频率范围内具有较高的精度和计算效率，对一段受到大范围随机激励的液压管道进行了比较。液压管道系统的系统参数研究调查了各种边界条件、流体速度和多点激励相干性的影响。数值算例通过与基于有限元方法的随机振动分析相比，在较宽的频率范围内具有较高的精度和计算效率，对一段受到大范围随机激励的液压管道进行了比较。液压管道系统的系统参数研究调查了各种边界条件、流体速度和多点激励相干性的影响。