Topology Optimization for Pipe Vibration Reduction Considering Nonproportional Damping via Iterative Modal Superposition

High‐frequency vibration in piping systems poses a significant risk of fatigue failure. While applying high‐damping alloy layers is an effective mitigation strategy, optimizing their layout is crucial. However, the localized application of damping materials induces significant nonproportional damping, a phenomenon presenting a major challenge for dynamic topology optimization, as conventional methods are either inaccurate or computationally prohibitive. This study overcomes this challenge by introducing a novel topology optimization framework that accurately and efficiently handles nonproportional damping effects. The core of the framework is the integration of an iterative modal superposition method for dynamic analysis, enabling its effective use within an optimization loop. This methodology was applied to optimize an M2052 Mn–Cu damping layer on a steel pipe to suppress shell vibration in the 1200–1400 Hz band. Numerical results show that the proposed method yields a physically rational layout in high modal strain energy regions, unlike the simplified proportional damping assumption. Experimental validation confirmed the method’s effectiveness: the optimized design, using 70% less material, achieved peak acceleration reductions (up to 84.32%) comparable to a fully covered configuration, highlighting its significant engineering value.