Cross-Fidelity Verification of Tuned Mass Damper Design for Slender Steel Chimneys: From 2-DOF to Solid Elements

Abstract

A tuned mass damper (TMD) is the standard mitigation for the vortex-induced vibration of steel chimneys, yet it is sized on one low-order model and never checked at higher fidelity. We verify a TMD design for a 60 m steel chimney of 3 m diameter and 5 mm wall (D/t=600) across three fidelities: a Den Hartog absorber, a beam model with a Hirsch ring, and a three-dimensional solid model. They agree to within 0.34% on the first bending frequency and 0.43% on the two Den Hartog modes, and four results follow. On an affordable mesh, fully integrated hexahedra lock and mistune the absorber beyond the tolerance box, costing 32.5% on the peak. Fatigue sizes the device, not the peak response: the customary 3% mass ratio leaves the controlled stress range above the EN 1993-1-9 cut-off, and unlimited life takes about 10%. Across four seismic regions the earthquake does not size the mass, which wind governs through fatigue, but it sizes the stroke: at the two most seismic sites the conventional ring needs 1.6 and 3.3 times the installed clearance, 2.8 and 5.7 once sized for fatigue. Fifteen geometries place the validity limit at (L/D)2/(D/t)≈0.3, below which shell modes precede bending.