This paper introduces a computationally efficient global sensitivity analysis method for quantifying the influence of uncertain clamp support conditions on the natural frequencies of aero-engine pipe systems. The dynamic model is based on a three-dimensional Timoshenko beam finite element formulation, with clamps represented as distributed spring elements possessing anisotropic stiffness. To overcome the prohibitive cost of traditional Monte Carlo simulation, the multiplicative dimensional reduction method (M-DRM) is integrated with variance decomposition theory. This approach approximates the high-dimensional frequency response function as a product of univariate components, enabling rapid computation of Sobol’ sensitivity indices with a computational cost reduced by three orders of magnitude. Numerical case studies on a planar Z-shaped pipe and a spatial series-parallel configuration reveal that clamp position parameters dominate the system’s natural frequency characteristics. For critical clamps, Sobol’ indices exceed 0.8 across multiple vibration modes, whereas stiffness parameters exhibit negligible influence. The proposed methodology provides a rigorous and efficient tool for identifying dominant uncertainty sources, guiding tolerance allocation in manufacturing, and informing robust support design for vibration-sensitive piping systems.
Shi et al. (Thu,) studied this question.