Vibration Control through Multiple Tuned Mass Dampers

Abstract

Structural responses under dynamic loading contain multiple frequency components, which can excite several vibration modes simultaneously. Among passive dynamic vibration absorbers (DVAs), tuned mass dampers (TMDs) are the most widely used. In practice, a single TMD (STMD) is typically installed at the roof to target the fundamental mode, leaving higher modes insufficiently controlled and limiting overall effectiveness. This study investigates multi-TMD (MTMD) configurations to enhance multimodal vibration mitigation. Three layouts are examined: (i) distributed MTMDs (d-MTMDs), placed according to mode shapes; (ii) arbitrary MTMDs (a-MTMDs), positioned without placement rules; and (iii) roof-clustered MTMDs (MTMDs@top), all devices located at the top. The STMD is tested on a 20-degree-of-freedom (DOF) shear-building model, while all MTMD configurations are applied to an 80-DOF benchmark structure. Governing equations of motion are derived analytically and solved numerically using the Newmark-β linear acceleration method. The 20-DOF system is subjected to recorded earthquake excitations, and the 80-DOF to wind histories. Performance is evaluated using square-root-sum-of-squares (SRSS) and root-mean-square (RMS) metrics. Results show that d-MTMDs achieve the most effective multimodal control, whereas a-MTMDs provide comparable global reductions to MTMDs@top but less consistent mitigation in upper stories.

Keywords: Single TMD; Multiple TMDs; Shear-building model; Newmark-β integration method; Multimodal vibration control; earthquake excitations; wind histories