Comparative FEM Analysis of Two Beam-Type TMD Sizing Methods Under Motor-Induced Vibrations in a Steel Frame

Abstract Background Industrial steel frames supporting unbalanced motors are susceptible to resonant vibrations that compromise structural safety. While beam-type Tuned Mass Dampers (TMDs) offer a continuous absorber solution, the relative merits of the two primary sizing approaches—the stiffness-driven Maximum Deflection Method (MDM) and the mass-driven Mass Ratio Method (MRM)—have not been compared under realistic multi-directional excitation. Methods The coupled frame-TMD system was evaluated through high-fidelity shell element simulations (SHELL181) in ANSYS. Modal, harmonic, and transient analyses were conducted across eight continuous absorber configurations. These devices were sized using both MDM and MRM paradigms and precisely tuned to the structure's fundamental frequency to evaluate performance under multi-directional loading states. Results MDM-sized devices consistently outperformed their MRM counterparts. The lightweight DM4 configuration (MDM) reduced peak acceleration by 72.53% under a 1 N harmonic sweep while minimizing cross-axis disturbance, and the DM1 configuration achieved up to 99.05% attenuation under a 30 N resonant load. Conversely, MRM configurations proved less efficient due to suboptimal tip-to-stem mass distributions that resulted in severe detuning. Conclusions Stiffness-driven optimization (MDM) achieves superior, more stable multi-axis vibration control with lower mass requirements compared to traditional mass-driven methods. These findings provide a quantitative and mass-efficient reference for designing continuous dynamic absorbers in space-constrained industrial structures.